Effect of Time Delay and Evolutionarily Stable Strategy

In this paper, a simple two-phenotype model with time delay is investigated. The main results are that: (i) the stability of the interior equilibrium point of the pure strategy model not only depends on the property of the payoff matrix but also the effect of time delay; (ii) the conditions of the evolutionarily stable strategy in the two-phenotype model with time delay are completely identical with the conditions in the two-phenotype model with no time delay; and (iii) a mixed evolutionarily stable strategy can be an unstable equilibrium state of the population in the two-phenotype model with time delay.