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Eco-evolutionary dynamics with environmental feedback occur when individual action modifies both the relative abundance of strategies and surrounding environment. The feedback mechanism can be captured by a function from actions of the population to the environment. As for the evolution of strategies, replicator equation common models it based on the natural selection. However, strategies spread not only by natural selection but also by imitation in evolutionary game. Specifically, Fermi process, as a kind of imitation rule, is generally adopted by individuals. This work propose a class of ecoevolutionary dynamics where strategies coevolve with the environment by general imitation functions. Then the condition under which a limit cycle may occur in the system is obtained, which can never be present in coupled replicator dynamics with environment. Further, the dynamical outcomes can be devided into four cases and compare with the classical system in detail. |
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Keywords:nonlinear dynamics;co-evolutionary dynamics; stability; heteroclinic cycle |
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