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Evolutionary dynamics on one-dimensional cycles with shifting mechanism and tiny mutation rate. (English) Zbl 1340.91015

Summary: In this paper, we study the impact of tiny mutation on the evolutionary dynamics on one-dimensional cycles with shifting mechanism. The evolutionary success is evaluated by investigating the stationary distribution of the ergodic process with the idea of viscosity solutions. The cooperative behaviors in ecosystem and social system are briefly discussed by applying the results to the prisoner’s dilemma game.

MSC:

91A22 Evolutionary games
91A15 Stochastic games, stochastic differential games
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