EvoLudoLab: Ecological Public Goods Game - Bautin: Difference between revisions
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{{EvoLudoLab:EcoPGG| | {{EvoLudoLab:EcoPGG| | ||
options="--module ePGG --model ODE --run --delay 100 --view Strategies_-_2D_Phase_Plane --timestep 0.2 -- | options="--module ePGG --model ODE --run --delay 100 --view Strategies_-_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"| | ||
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. | ||