Bifurcation and Pattern Formation in an Activator-Inhibitor Model with Non-local Dispersal.
Bull Math Biol
; 84(12): 140, 2022 10 29.
Article
em En
| MEDLINE
| ID: mdl-36308606
ABSTRACT
In this paper, by approximating the non-local spatial dispersal equation by an associated reaction-diffusion system, an activator-inhibitor model with non-local dispersal is transformed into a reaction-diffusion system coupled with one ordinary differential equation. We prove that, to some extent, the non-locality-induced instability of the non-local system can be regarded as diffusion-driven instability of the reaction-diffusion system for sufficiently small perturbation. We study the structure of the spectrum of the corresponding linearized operator, and we use linear stability analysis and steady-state bifurcations to show the existence of non-constant steady states which generates non-homogeneous spatial patterns. As an example of our results, we study the bifurcation and pattern formation of a modified Klausmeier-Gray-Scott model of water-plant interaction.
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01-internacional
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MEDLINE
Assunto principal:
Conceitos Matemáticos
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Modelos Biológicos
Idioma:
En
Ano de publicação:
2022
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Article