Nonlinear eco-evolutionary games with global environmental fluctuations and local environmental feedbacks
Fig 5
Emergence of cyclic evolution of group cooperation and local environment under periodically changing global environments given by w1(t).
Panel (a) shows local game-environment evolution similar to Fig 4. Panel (b) displays four typical dynamic trajectories in detail, particularly the interior closed yet irregular orbits. The last row presents time evolution of the frequency of cooperators x and the multiplication factor of cooperators rc under different initial conditions, corresponding to the colored trajectories in panel (b). Results show that the formation of cyclic evolution under discrete global environment is due to the fact that the two fixed points are in the mutual attraction domains (b-d). Parameters: N = 4, α = 1.5, β = 3.5, θ = 1, rd = 1.2, T = 10π, ϵ = 4.