Limit cycles analysis and control of evolutionary game dynamics with environmental feedback

Recently, an evolutionary game dynamics model taking into account the environmental feedback has been proposed to describe co-evolution of strategic actions a population individuals and state surrounding environment; correspondingly range interesting dynamic behaviors have reported. In this paper, we provide new theoretical insight such discuss control options. Instead standard replicator dynamics, use more realistic comprehensive replicator–mutator evolution population. After integrating environment feedback, study effect mutations on resulting closed-loop system dynamics. We prove conditions for two types bifurcations, Hopf bifurcation Heteroclinic bifurcation, both which result in stable limit cycles. These cycles not identified existing works, further that are fact persistent large parameter space almost globally stable. end, intuitive policy based incentives is applied, effectiveness examined by analysis simulations.