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arXiv · 2312.10231

Two simple criterion to prove the existence of patterns in reaction-diffusion models of two components

Francisco J. Vielma-Leal·Miguel A. D. R. Palma·Miguel Montenegro-Concha
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Abstract

The aim of this work is to study the effect of diffusion on the stability of the equilibria in a general two-components reaction-diffusion system with Neumann boundary conditions in the space of continuous functions. As by product, we establish sufficient conditions on the diffusive coefficients and other parameters for such a reaction-diffusion model to exhibit patterns and we analyze their stability. We apply the results obtained in this paper to explore under which parameters values a Turing bifurcation can occur, given rise to non uniform stationary solutions (patterns) for a reaction-diffusion predator-prey model with variable mortality and Hollyn's type II functional response.

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Francisco J. Vielma-Leal, Miguel A. D. R. Palma, Miguel Montenegro-Concha. 2023-12-15. Two simple criterion to prove the existence of patterns in reaction-diffusion models of two components. https://arxiv.org/abs/2312.10231

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