Evolutionary Games and Population Dynamics/Well-mixed populations: Difference between revisions

{{InCharge|author1=Christoph Hauert}}

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[[Image:Well-mixed Ecological PGG - Bifurcations.png|thumb|300px|Bifurcations and dynamical regimes (separated by dashed lines) in heterogeneous populations of cooperators and defectors interacting in ecological public goods games with \(N=8\), \(b=1\), \(d=1.2\) and the multiplication factor \(r\) as the bifurcation parameter. The position of the fixed point \(Q\) changes with increasing \(r\) while the system undergoes a series of different bifurcations: \(Q\) enters on the top left for low \(r\) and leaves at the top right for high \(r\) (transcritical bifurcations). The different dynamical scenarios (a)-(f) apply depending on the location of \(Q\). In (a) and (f) \(Q\) is absent, in (b), (c) it is unstable and in (d), (e) it is stable. Between scenarios (c) and (d) a Hopf bifurcation occurs and over a very narrow range of \(r\), stable and unstable limit cycles can be observed.]]