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Evolutionary dynamics combines game theory and nonlinear dynamics to model competition in biological and social situations. The replicator equation is a standard paradigm in evolutionary dynamics. The growth rate of each strategy is its excess fitness: the deviation of its fitness from the average. The game-theoretic aspect of the model lies in the choice of fitness function, which is determined by...
This paper concerns the dynamics of the following nonlinear differential-delay equation:in which T is the delay and is a coefficient of self-feedback. Using numerical integration, continuation programs and bifurcation theory, we show that this system exhibits a wide range of dynamical phenomena, including Hopf and pitchfork bifurcations, limit cycle folds and relaxation oscillations. It is shown that...
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