Abstract
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.
Highlights
Evolutionary game dynamics propose a basic framework to study and predict the evolutionary behavior in physics [1, 2], biology [3,4,5], economics [6, 7], and social networks [8, 9]
Our results show that the interior equilibrium in imitative dynamics is asymptotically stable when the delay is smaller than the critical value
5 Conclusion In this paper, the stability of the neutrally stable strategy (NSS) in two-community has been investigated for the imitative dynamics with diverse delays
Summary
Evolutionary game dynamics propose a basic framework to study and predict the evolutionary behavior in physics [1, 2], biology [3,4,5], economics [6, 7], and social networks [8, 9]. Hu et al [25] researched the imitative dynamics with discrete delay, they obtained some sufficient conditions of stability in imitative dynamics. In social networks and biology [31, 32], the population is formed by different communities which can be called clusters In this case, the individual may interact with an opponent inside or outside the community. Nesrune et al [32] considered evolutionary dynamics in interacting communities, they researched the two-community two-strategy model and obtained some sufficient conditions for stability. We research the effect of diversity delay on the stability in a new model and obtain three sufficient conditions for stability in imitative dynamics with different delays.
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