Oscillatory dynamics in rock-paper-scissors games with mutations.
We study the oscillatory dynamics in the generic three-species rock-paper-scissors games with mutations. In the mean-field limit, different behaviors are found: (a) for high mutation rate, there is a stable interior fixed point with coexistence of all species; (b) for low mutation rates, there is a region of the parameter space characterized by a limit cycle resulting from a Hopf bifurcation; (c) in the absence of mutations, there is a region where heteroclinic cycles yield oscillations of large amplitude (not robust against noise). After a discussion on the main properties of the mean-field dynamics, we investigate the stochastic version of the model within an individual-based formulation. Demographic fluctuations are therefore naturally accounted and their effects are studied using a diffusion theory complemented by numerical simulations. It is thus shown that persistent erratic oscillations (quasi-cycles) of large amplitude emerge from a noise-induced resonance phenomenon. We also analytically and numerically compute the average escape time necessary to reach a (quasi-)cycle on which the system oscillates at a given amplitude.
Mobilia
Mauro
M
Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK. M.Mobilia@leeds.ac.uk
D000465:Algorithms; D044822:Biodiversity; D005075:Biological Evolution; D003198:Computer Simulation; D017753:Ecosystem; D005716:Game Theory; D007700:Kinetics; D016014:Linear Models; D008390:Markov Chains; D008954:Models, Biological; D009154:Mutation / Q000502:physiology*; D017711:Nonlinear Dynamics; D011157:Population Dynamics; D012098:Reproduction / Q000502:physiology; D012641:Selection, Genetic / Q000502:physiology; D013269:Stochastic Processes