Open AccessDiffusion-driven instability of both the equilibrium solution and the periodic solutions for the diffusive Sporns-Seelig model
Author(s) -
Nan Xiang,
Aying Wan,
Hongyan Lin
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022043
Subject(s) - instability , homogeneous , reaction–diffusion system , bounded function , diffusion , neumann boundary condition , constant (computer programming) , mathematical analysis , domain (mathematical analysis) , mathematics , boundary value problem , periodic boundary conditions , physics , thermodynamics , mechanics , computer science , programming language
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.