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Abstract
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We study the evolutionary dynamic of population, composed of two kinds of individuals, distributed randomly. In this game, evolution takes place in different periods of time between individuals frequently. We present a continuous nonlinear operator, which describes and fulfills this discrete time evolutionary game. Furthermore, we set up the adequate mathematical framework to obtain the fixed point of this operator. Based on this equilibrium state of the evolutionary operator, it is proved the possessions of the individuals vanish.
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