Stability analysis of imitative dynamics in two-community with multiple delays

Evolutionary game dynamics has become a hot topic in recent years. In this paper, we combine game theory and dynamical systems to investigate the stability of imitative dynamics in two-community with different kinds of delays. First, we establish a new model of imitative dynamics in two-community. Then, three sufficient conditions of the asymptotical stability for the neutrally stable strategy of the imitative dynamics are obtained. Finally, numerical simulations are consistent with the theoretical analysis.