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arXiv · 1803.00774

Competition in periodic media: III -- Existence \& stability of segregated periodic coexistence states

Léo Girardin·Alessandro Zilio
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Abstract

In this paper we consider a system of parabolic reaction-diffusion equations with strong competition and two related scalar reaction-diffusion equations. We are mainly concerned with the case of periodic coefficients and periodic solutions. We show that, for sufficiently large periods, these models have stationary, non-constant, fully non-trivial and stable solutions. We compare our results with already known results about the existence and non-existence of such solutions. Finally, we provide ecological interpretations for these results in terms of resistance against an invasion.

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Léo Girardin, Alessandro Zilio. 2018-03-02. Competition in periodic media: III -- Existence \& stability of segregated periodic coexistence states. https://arxiv.org/abs/1803.00774

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