https://wiki.evoludo.org/index.php?action=history&feed=atom&title=EvoLudoLab%3A_Ecological_Public_Goods_Game_-_Bautin 2026-04-24T15:29:43Z Revision history for this page on the wiki MediaWiki 1.42.1 https://wiki.evoludo.org/index.php?title=EvoLudoLab:_Ecological_Public_Goods_Game_-_Bautin&diff=3037&oldid=prev 2026-02-19T07:09:11Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en-CA"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 00:09, 19 February 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EvoLudoLab:EcoPGG|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EvoLudoLab:EcoPGG|</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>options="--module ePGG --model ODE --run --delay 100 --view <del style="font-weight: bold; text-decoration: none;">Strategies_</del>-_2D_Phase_Plane --timestep 0.2 --init frequencies 1,9,90 --fitnessmap static 0,1 --cost 1.0 --interest 3.05 --groupsize 12 --deathrate 0.5 --points 0.135,0.068,0.798"|</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>options="--module ePGG --model ODE --run --delay 100 --view <ins style="font-weight: bold; text-decoration: none;">Traits_</ins>-_2D_Phase_Plane --timestep 0.2 --init frequencies 1,9,90 --fitnessmap static 0,1 --cost 1.0 --interest 3.05 --groupsize 12 --deathrate 0.5 --points 0.135,0.068,0.798"|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here \(N = 12\)) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try \(r = 3.04\)). In fact, this is a Bautin bifurcation with \(N\) as the second parameter. Increasing \(N\) turns the super-critical Hopf bifurcation into a subcritical one.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here \(N = 12\)) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try \(r = 3.04\)). In fact, this is a Bautin bifurcation with \(N\) as the second parameter. Increasing \(N\) turns the super-critical Hopf bifurcation into a subcritical one.</div></td></tr> </table>

Hauert https://wiki.evoludo.org/index.php?title=EvoLudoLab:_Ecological_Public_Goods_Game_-_Bautin&diff=2922&oldid=prev 2024-08-12T21:42:17Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en-CA"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:42, 12 August 2024</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EvoLudoLab:EcoPGG|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EvoLudoLab:EcoPGG|</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>options="--module ePGG --model ODE --run --delay 100 --view Strategies_-_2D_Phase_Plane --timestep 0.2 --<del style="font-weight: bold; text-decoration: none;">inittype </del>frequencies 1,9,90 --fitnessmap static 0,1 --cost 1.0 --interest 3.05 --groupsize 12 --deathrate 0.5 --points 0.135,0.068,0.798"|</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>options="--module ePGG --model ODE --run --delay 100 --view Strategies_-_2D_Phase_Plane --timestep 0.2 --<ins style="font-weight: bold; text-decoration: none;">init </ins>frequencies 1,9,90 --fitnessmap static 0,1 --cost 1.0 --interest 3.05 --groupsize 12 --deathrate 0.5 --points 0.135,0.068,0.798"|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here \(N = 12\)) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try \(r = 3.04\)). In fact, this is a Bautin bifurcation with \(N\) as the second parameter. Increasing \(N\) turns the super-critical Hopf bifurcation into a subcritical one.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here \(N = 12\)) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try \(r = 3.04\)). In fact, this is a Bautin bifurcation with \(N\) as the second parameter. Increasing \(N\) turns the super-critical Hopf bifurcation into a subcritical one.</div></td></tr> </table>

Hauert https://wiki.evoludo.org/index.php?title=EvoLudoLab:_Ecological_Public_Goods_Game_-_Bautin&diff=2788&oldid=prev 2024-08-04T19:48:06Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en-CA"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:48, 4 August 2024</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EvoLudoLab:EcoPGG|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EvoLudoLab:EcoPGG|</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>options="--<del style="font-weight: bold; text-decoration: none;">game </del>ePGG --model ODE --run --delay 100 --view Strategies_-_2D_Phase_Plane --<del style="font-weight: bold; text-decoration: none;">reportfreq </del>0.2 --<del style="font-weight: bold; text-decoration: none;">init </del>1,9,90 --<del style="font-weight: bold; text-decoration: none;">inittype frequencies --mutation </del>0<del style="font-weight: bold; text-decoration: none;">.0 --basefit 0.0 --selection </del>1<del style="font-weight: bold; text-decoration: none;">.0 --fitnessmap static </del>--cost 1.0 --interest 3.05 --groupsize 12 --deathrate 0.5"|</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>options="--<ins style="font-weight: bold; text-decoration: none;">module </ins>ePGG --model ODE --run --delay 100 --view Strategies_-_2D_Phase_Plane --<ins style="font-weight: bold; text-decoration: none;">timestep </ins>0.2 --<ins style="font-weight: bold; text-decoration: none;">inittype frequencies </ins>1,9,90 --<ins style="font-weight: bold; text-decoration: none;">fitnessmap static </ins>0<ins style="font-weight: bold; text-decoration: none;">,</ins>1 --cost 1.0 --interest 3.05 --groupsize 12 --deathrate 0.5 <ins style="font-weight: bold; text-decoration: none;">--points 0.135,0.068,0.798</ins>"|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here \(N = 12\)) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try \(r = 3.04\)). In fact, this is a Bautin bifurcation with \(N\) as the second parameter. Increasing \(N\) turns the super-critical Hopf bifurcation into a subcritical one.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here \(N = 12\)) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try \(r = 3.04\)). In fact, this is a Bautin bifurcation with \(N\) as the second parameter. Increasing \(N\) turns the super-critical Hopf bifurcation into a subcritical one.</div></td></tr> </table>

Hauert https://wiki.evoludo.org/index.php?title=EvoLudoLab:_Ecological_Public_Goods_Game_-_Bautin&diff=2696&oldid=prev 2023-10-13T17:16:43Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en-CA"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:16, 13 October 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EvoLudoLab:EcoPGG|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EvoLudoLab:EcoPGG|</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>options="--game ePGG --run --delay <del style="font-weight: bold; text-decoration: none;">200 </del>--view Strategies_-_2D_Phase_Plane --reportfreq 0.2 --<del style="font-weight: bold; text-decoration: none;">popsize 10000 --popupdate D --playerupdate I --geometry M --intertype a --numinter </del>1 --<del style="font-weight: bold; text-decoration: none;">reprotype a1 --initfreqs 1:9:90 </del>--mutation 0.0 --basefit 0.0 --selection 1.0 --fitnessmap static --cost 1.0 --interest 3.05 --groupsize 12 --deathrate 0.5"|</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>options="--game ePGG <ins style="font-weight: bold; text-decoration: none;">--model ODE </ins>--run --delay <ins style="font-weight: bold; text-decoration: none;">100 </ins>--view Strategies_-_2D_Phase_Plane --reportfreq 0.2 --<ins style="font-weight: bold; text-decoration: none;">init </ins>1<ins style="font-weight: bold; text-decoration: none;">,9,90 </ins>--<ins style="font-weight: bold; text-decoration: none;">inittype frequencies </ins>--mutation 0.0 --basefit 0.0 --selection 1.0 --fitnessmap static --cost 1.0 --interest 3.05 --groupsize 12 --deathrate 0.5"|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here \(N = 12\)) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try \(r = 3.04\)). In fact, this is a Bautin bifurcation with \(N\) as the second parameter. Increasing \(N\) turns the super-critical Hopf bifurcation into a subcritical one.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here \(N = 12\)) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try \(r = 3.04\)). In fact, this is a Bautin bifurcation with \(N\) as the second parameter. Increasing \(N\) turns the super-critical Hopf bifurcation into a subcritical one.</div></td></tr> </table>

Hauert https://wiki.evoludo.org/index.php?title=EvoLudoLab:_Ecological_Public_Goods_Game_-_Bautin&diff=2578&oldid=prev 2019-11-11T02:56:29Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en-CA"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:56, 10 November 2019</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EvoLudoLab:EcoPGG|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EvoLudoLab:EcoPGG|</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>options="--game ePGG --run --delay 200 --view Strategies_-_2D_Phase_Plane --reportfreq 0.2 --popsize 10000 --popupdate D --playerupdate I --geometry M --intertype a --numinter 1 --reprotype a1 --initfreqs <del style="font-weight: bold; text-decoration: none;">5</del>:<del style="font-weight: bold; text-decoration: none;">70</del>:<del style="font-weight: bold; text-decoration: none;">25 </del>--mutation 0.0 --basefit 0.0 --selection 1.0 --fitnessmap static --cost 1.0 --interest 3.05 --groupsize 12 --deathrate 0.5"|</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>options="--game ePGG --run --delay 200 --view Strategies_-_2D_Phase_Plane --reportfreq 0.2 --popsize 10000 --popupdate D --playerupdate I --geometry M --intertype a --numinter 1 --reprotype a1 --initfreqs <ins style="font-weight: bold; text-decoration: none;">1</ins>:<ins style="font-weight: bold; text-decoration: none;">9</ins>:<ins style="font-weight: bold; text-decoration: none;">90 </ins>--mutation 0.0 --basefit 0.0 --selection 1.0 --fitnessmap static --cost 1.0 --interest 3.05 --groupsize 12 --deathrate 0.5"|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here \(N = 12\)) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try \(r = 3.04\)). In fact, this is a Bautin bifurcation with \(N\) as the second parameter. Increasing \(N\) turns the super-critical Hopf bifurcation into a subcritical one.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here \(N = 12\)) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try \(r = 3.04\)). In fact, this is a Bautin bifurcation with \(N\) as the second parameter. Increasing \(N\) turns the super-critical Hopf bifurcation into a subcritical one.</div></td></tr> </table>

Hauert https://wiki.evoludo.org/index.php?title=EvoLudoLab:_Ecological_Public_Goods_Game_-_Bautin&diff=2577&oldid=prev 2019-11-11T02:55:15Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en-CA"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:55, 10 November 2019</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EvoLudoLab:EcoPGG|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EvoLudoLab:EcoPGG|</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>options="--game ePGG --run --delay 200 --view Strategies_-_2D_Phase_Plane --reportfreq 0.2 --popsize 10000 --popupdate D --playerupdate I --geometry M --intertype a --numinter 1 --reprotype a1 --initfreqs 70<del style="font-weight: bold; text-decoration: none;">:5</del>:25 --mutation 0.0 --basefit 0.0 --selection 1.0 --fitnessmap static --cost 1.0 --interest 3.05 --groupsize 12 --deathrate 0.5"|</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>options="--game ePGG --run --delay 200 --view Strategies_-_2D_Phase_Plane --reportfreq 0.2 --popsize 10000 --popupdate D --playerupdate I --geometry M --intertype a --numinter 1 --reprotype a1 --initfreqs <ins style="font-weight: bold; text-decoration: none;">5:</ins>70:25 --mutation 0.0 --basefit 0.0 --selection 1.0 --fitnessmap static --cost 1.0 --interest 3.05 --groupsize 12 --deathrate 0.5"|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here \(N = 12\)) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try \(r = 3.04\)). In fact, this is a Bautin bifurcation with \(N\) as the second parameter. Increasing \(N\) turns the super-critical Hopf bifurcation into a subcritical one.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here \(N = 12\)) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try \(r = 3.04\)). In fact, this is a Bautin bifurcation with \(N\) as the second parameter. Increasing \(N\) turns the super-critical Hopf bifurcation into a subcritical one.</div></td></tr> </table>

Hauert https://wiki.evoludo.org/index.php?title=EvoLudoLab:_Ecological_Public_Goods_Game_-_Bautin&diff=2576&oldid=prev 2019-11-11T02:54:30Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en-CA"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:54, 10 November 2019</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EvoLudoLab:EcoPGG|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EvoLudoLab:EcoPGG|</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>options="--game ePGG --run --delay 200 --view Strategies_-<del style="font-weight: bold; text-decoration: none;">_Phase_2D </del>--reportfreq 0.2 --popsize 10000 --popupdate D --playerupdate I --geometry M --intertype a --numinter 1 --reprotype a1 --initfreqs 70:5:25 --mutation 0.0 --basefit 0.0 --selection 1.0 --fitnessmap static --cost 1.0 --interest 3.05 --groupsize 12 --deathrate 0.5"|</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>options="--game ePGG --run --delay 200 --view Strategies_-<ins style="font-weight: bold; text-decoration: none;">_2D_Phase_Plane </ins>--reportfreq 0.2 --popsize 10000 --popupdate D --playerupdate I --geometry M --intertype a --numinter 1 --reprotype a1 --initfreqs 70:5:25 --mutation 0.0 --basefit 0.0 --selection 1.0 --fitnessmap static --cost 1.0 --interest 3.05 --groupsize 12 --deathrate 0.5"|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here \(N = 12\)) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try \(r = 3.04\)). In fact, this is a Bautin bifurcation with \(N\) as the second parameter. Increasing \(N\) turns the super-critical Hopf bifurcation into a subcritical one.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here \(N = 12\)) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try \(r = 3.04\)). In fact, this is a Bautin bifurcation with \(N\) as the second parameter. Increasing \(N\) turns the super-critical Hopf bifurcation into a subcritical one.</div></td></tr> </table>

Hauert https://wiki.evoludo.org/index.php?title=EvoLudoLab:_Ecological_Public_Goods_Game_-_Bautin&diff=2575&oldid=prev 2019-11-11T02:53:48Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en-CA"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:53, 10 November 2019</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EvoLudoLab:EcoPGG|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EvoLudoLab:EcoPGG|</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>options="--run --delay 200 --view Strategies_-_Phase_2D --reportfreq 0.2 --popsize 10000 --popupdate D --playerupdate I --geometry M --intertype a --numinter 1 --reprotype a1 --initfreqs 70:5:25 --mutation 0.0 --basefit 0.0 --selection 1.0 --fitnessmap static --cost 1.0 --interest 3.05 --groupsize 12 --deathrate 0.5"|</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>options="<ins style="font-weight: bold; text-decoration: none;">--game ePGG </ins>--run --delay 200 --view Strategies_-_Phase_2D --reportfreq 0.2 --popsize 10000 --popupdate D --playerupdate I --geometry M --intertype a --numinter 1 --reprotype a1 --initfreqs 70:5:25 --mutation 0.0 --basefit 0.0 --selection 1.0 --fitnessmap static --cost 1.0 --interest 3.05 --groupsize 12 --deathrate 0.5"|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here \(N = 12\)) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try \(r = 3.04\)). In fact, this is a Bautin bifurcation with \(N\) as the second parameter. Increasing \(N\) turns the super-critical Hopf bifurcation into a subcritical one.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here \(N = 12\)) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try \(r = 3.04\)). In fact, this is a Bautin bifurcation with \(N\) as the second parameter. Increasing \(N\) turns the super-critical Hopf bifurcation into a subcritical one.</div></td></tr> </table>

Hauert https://wiki.evoludo.org/index.php?title=EvoLudoLab:_Ecological_Public_Goods_Game_-_Bautin&diff=2574&oldid=prev 2019-11-11T02:52:57Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en-CA"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:52, 10 November 2019</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EvoLudoLab:EcoPGG|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{EvoLudoLab:EcoPGG|</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>options="--run <del style="font-weight: bold; text-decoration: none;">--AA </del>--delay 200 --view <del style="font-weight: bold; text-decoration: none;">Strategy_</del>-_Phase_2D <del style="font-weight: bold; text-decoration: none;">--no3D </del>--reportfreq 0.2 --popsize 10000 --popupdate D --playerupdate I <del style="font-weight: bold; text-decoration: none;">--updateprob 1.0 </del>--geometry M --intertype a --numinter 1 --reprotype a1 --initfreqs 70:5:25 --mutation 0.0 --basefit <del style="font-weight: bold; text-decoration: none;">1</del>.0 --selection 1.0 --cost 1.0 --interest 3.05 --groupsize 12 <del style="font-weight: bold; text-decoration: none;">--birthrate 0.0 </del>--deathrate 0.5"|</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>options="--run --delay 200 --view <ins style="font-weight: bold; text-decoration: none;">Strategies_</ins>-_Phase_2D --reportfreq 0.2 --popsize 10000 --popupdate D --playerupdate I --geometry M --intertype a --numinter 1 --reprotype a1 --initfreqs 70:5:25 --mutation 0.0 --basefit <ins style="font-weight: bold; text-decoration: none;">0</ins>.0 --selection 1.0 <ins style="font-weight: bold; text-decoration: none;">--fitnessmap static </ins>--cost 1.0 --interest 3.05 --groupsize 12 --deathrate 0.5"|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here \(N = 12\)) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try \(r = 3.04\)). In fact, this is a Bautin bifurcation with \(N\) as the second parameter. Increasing \(N\) turns the super-critical Hopf bifurcation into a subcritical one.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here \(N = 12\)) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try \(r = 3.04\)). In fact, this is a Bautin bifurcation with \(N\) as the second parameter. Increasing \(N\) turns the super-critical Hopf bifurcation into a subcritical one.</div></td></tr> </table>

Hauert https://wiki.evoludo.org/index.php?title=EvoLudoLab:_Ecological_Public_Goods_Game_-_Bautin&diff=1164&oldid=prev 2012-03-31T09:51:36Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en-CA"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 02:51, 31 March 2012</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{<del style="font-weight: bold; text-decoration: none;">VirtualLab</del>:EcoPGG|</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{<ins style="font-weight: bold; text-decoration: none;">EvoLudoLab</ins>:EcoPGG|</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>options="--run --delay 200 --view <del style="font-weight: bold; text-decoration: none;">3 </del>--reportfreq 0.2 --popsize 10000 --popupdate D --playerupdate <del style="font-weight: bold; text-decoration: none;">i </del>--updateprob 1<del style="font-weight: bold; text-decoration: none;">.0 --switchpref 0</del>.0 --geometry M --intertype <del style="font-weight: bold; text-decoration: none;">a11 </del>--numinter 1 --reprotype a1 --initfreqs 70:5:25 --mutation 0.0 --basefit 1.0 --selection 1.0 --cost 1.0 --interest 3.05 --birthrate 0.0 --deathrate 0.5"|</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>options="--run <ins style="font-weight: bold; text-decoration: none;">--AA </ins>--delay 200 --view <ins style="font-weight: bold; text-decoration: none;">Strategy_-_Phase_2D --no3D </ins>--reportfreq 0.2 --popsize 10000 --popupdate D --playerupdate <ins style="font-weight: bold; text-decoration: none;">I </ins>--updateprob 1.0 --geometry M --intertype <ins style="font-weight: bold; text-decoration: none;">a </ins>--numinter 1 --reprotype a1 --initfreqs 70:5:25 --mutation 0.0 --basefit 1.0 --selection 1.0 --cost 1.0 --interest 3.05 <ins style="font-weight: bold; text-decoration: none;">--groupsize 12 </ins>--birthrate 0.0 --deathrate 0.5"|</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>title=Stable focus &#039;&#039;Q&#039;&#039; - multiple stable and unstable limit cycles (Bautin bifurcation)|</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here <del style="font-weight: bold; text-decoration: none;">&lt;math&gt;</del>N = 12<del style="font-weight: bold; text-decoration: none;">&lt;/math&gt;</del>) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try <del style="font-weight: bold; text-decoration: none;">&lt;math&gt;</del>r = 3.04<del style="font-weight: bold; text-decoration: none;">&lt;/math&gt;</del>). In fact, this is a Bautin bifurcation with <del style="font-weight: bold; text-decoration: none;">&lt;math&gt;</del>N<del style="font-weight: bold; text-decoration: none;">&lt;/math&gt; </del>as the second parameter. Increasing <del style="font-weight: bold; text-decoration: none;">&lt;math&gt;</del>N<del style="font-weight: bold; text-decoration: none;">&lt;/math&gt; </del>turns the super-critical Hopf bifurcation into a subcritical one.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>doc=For larger group sizes (here <ins style="font-weight: bold; text-decoration: none;">\(</ins>N = 12<ins style="font-weight: bold; text-decoration: none;">\)</ins>) more complex dynamical scenarios occur. In this example, a pair of stable and unstable limit cycles occur on one side of the Hopf bifurcation and another stable limit cycle on the other side (try <ins style="font-weight: bold; text-decoration: none;">\(</ins>r = 3.04<ins style="font-weight: bold; text-decoration: none;">\)</ins>). In fact, this is a Bautin bifurcation with <ins style="font-weight: bold; text-decoration: none;">\(</ins>N<ins style="font-weight: bold; text-decoration: none;">\) </ins>as the second parameter. Increasing <ins style="font-weight: bold; text-decoration: none;">\(</ins>N<ins style="font-weight: bold; text-decoration: none;">\) </ins>turns the super-critical Hopf bifurcation into a subcritical one.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The parameters are <del style="font-weight: bold; text-decoration: none;">&lt;math&gt;</del>r = 3.05<del style="font-weight: bold; text-decoration: none;">&lt;/math&gt;</del>, <del style="font-weight: bold; text-decoration: none;">&lt;math&gt;</del>N = 12<del style="font-weight: bold; text-decoration: none;">&lt;/math&gt;</del>, <del style="font-weight: bold; text-decoration: none;">&lt;math&gt;</del>c = 1<del style="font-weight: bold; text-decoration: none;">&lt;/math&gt;</del>, <del style="font-weight: bold; text-decoration: none;">&lt;math&gt;</del>b = 0<del style="font-weight: bold; text-decoration: none;">&lt;/math&gt;</del>, <del style="font-weight: bold; text-decoration: none;">&lt;math&gt;</del>d = 0.5<del style="font-weight: bold; text-decoration: none;">&lt;/math&gt; </del>using numerical integration of the replicator equation. The Hopf-bifurcation occurs at <del style="font-weight: bold; text-decoration: none;">&lt;math&gt;</del>r_\text{Hopf} = 3.0414<del style="font-weight: bold; text-decoration: none;">&lt;/math&gt;</del>.}}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The parameters are <ins style="font-weight: bold; text-decoration: none;">\(</ins>r = 3.05<ins style="font-weight: bold; text-decoration: none;">\)</ins>, <ins style="font-weight: bold; text-decoration: none;">\(</ins>N = 12<ins style="font-weight: bold; text-decoration: none;">\)</ins>, <ins style="font-weight: bold; text-decoration: none;">\(</ins>c = 1<ins style="font-weight: bold; text-decoration: none;">\)</ins>, <ins style="font-weight: bold; text-decoration: none;">\(</ins>b = 0<ins style="font-weight: bold; text-decoration: none;">\)</ins>, <ins style="font-weight: bold; text-decoration: none;">\(</ins>d = 0.5<ins style="font-weight: bold; text-decoration: none;">\) </ins>using numerical integration of the replicator equation. The Hopf-bifurcation occurs at <ins style="font-weight: bold; text-decoration: none;">\(</ins>r_\text{Hopf} = 3.0414<ins style="font-weight: bold; text-decoration: none;">\)</ins>.}}</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category: Christoph Hauert]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category: Christoph Hauert]]</div></td></tr> </table>

Hauert