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Research Article | Open Access

Diffusion-driven instability of both the equilibrium solution and the periodic solutions for the diffusive Sporns-Seelig model

Nan Xiang1,2,3( ), Aying Wan3, Hongyan Lin3
College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin, Heilongjiang Province, 150001, China
College of Mathematical Sciences, Harbin Engineering University, Harbin, Heilongjiang Province, 150001, China
School of Mathematics and Statistics, Hulunbuir University, Hailar, Inner Mongolia, 021008, China
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Abstract

In this paper, a reaction-diffusion Sporn-Seelig model subject to homogeneous Neumann boundary condition in the one dimensional spatial open bounded domain is considered. Of our particular interests, we are concerned with diffusion-driven instability of both the positive constant equilibrium solution and the Hopf bifurcating spatially homogeneous periodic solutions. To strengthen our analytical results, we also include some numerical simulations. These results allow for the clearer understanding the mechanisms of the spatiotemporal pattern formations of this chemical reaction model.

Keywords

the diffusive Sporns-Seelig modelHopf bifurcationsspatially homogeneous periodic solutionsdiffusion-driven instabilityspatiotemporal patterns

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Electronic Research Archive
Volume 30 Issue 3,
March 2022
Pages 813-829
DOI: 10.3934/era.2022043

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Cite this article:
Xiang N, Wan A, Lin H. Diffusion-driven instability of both the equilibrium solution and the periodic solutions for the diffusive Sporns-Seelig model. Electronic Research Archive, 2022, 30(3): 813-829. https://doi.org/10.3934/era.2022043

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Received: 14 December 2021
Revised: 13 January 2022
Accepted: 09 February 2022
Published: 15 March 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)