Seasonal Floquet states in a game-driven evolutionary dynamics

Olena Tkachenko; Juzar Thingna; Sergey Denisov; Vasily Zaburdaev; Peter Hänggi

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arXiv · 1505.06726

Seasonal Floquet states in a game-driven evolutionary dynamics

Olena Tkachenko·Juzar Thingna·Sergey Denisov·Vasily Zaburdaev·Peter Hänggi

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Abstract

Mating preferences of many biological species are not constant but season-dependent. Within the framework of evolutionary game theory this can be modeled with two finite opposite-sex populations playing against each other following the rules that are periodically changing. By combining Floquet theory and the concept of quasi-stationary distributions, we reveal existence of metastable time-periodic states in the evolution of finite game-driven populations. The evolutionary Floquet states correspond to time-periodic probability flows in the strategy space which cannot be resolved within the mean-field framework. The lifetime of metastable Floquet states increases with the size $N$ of populations so that they become attractors in the limit $N \rightarrow \infty$.

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Olena Tkachenko, Juzar Thingna, Sergey Denisov, Vasily Zaburdaev, Peter Hänggi. 2015-08-12. Seasonal Floquet states in a game-driven evolutionary dynamics. https://arxiv.org/abs/1505.06726

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