Time delays in gene expression and evolutionary games
It is usually observed, and expected, that small time delays do not change behavior of dynamical systems and large time delays may cause oscillations. We will show that effects of time delays depend of their microscopic origins. A simple stochastic model of gene expression with delayed degradation will be presented. We will show that contrary to what was claimed, delayed degradation does not cause oscillations. We will also discuss models with self-repressed genes. We will show that microscopic models of evolutionary games with strategy-dependent time delays, in which payoffs appear some time after interactions of individuals, lead to a new type of replicator dynamics. Unlike in all previous models, stationary states of such dynamics, and in fact their number, depend on time delays.
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