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EvoLudoLab: Ecological Public Goods Game - Bautin: Difference between revisions
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EvoLudoLab: Ecological Public Goods Game - Bautin (view source)
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{{EvoLudoLab:EcoPGG| | {{EvoLudoLab:EcoPGG| | ||
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"| | options="--game ePGG --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"| | ||
title=Stable focus ''Q'' - multiple stable and unstable limit cycles (Bautin bifurcation)| | title=Stable focus ''Q'' - multiple stable and unstable limit cycles (Bautin bifurcation)| | ||
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. | 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. | ||
