Turing instability of the periodic solutions for the diffusive Sel'kov model with saturation effect. (February 2022)

• Record Type: Journal Article
• Authors: Wang, Pu; Gao, Yanbin
• Is Part Of: Nonlinear analysis. Volume 63(2022)
• Publication Date: 2022-02
• Subjects: Homogeneity breaking instability -- Spatially homogeneous periodic solutions -- Sel'kov model -- Chemical reactions; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103417
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we are concerned with the Turing instability of the spatially homogeneous Hopf bifurcating periodic solutions for the diffusive Sel'kov model with saturation effect. By using the center manifold theorem, normal form theory and the regularly perturbed theory, we derive a formula in terms of the diffusion rates to determine the Turing instability of the spatially homogeneous Hopf bifurcating periodic solutions in the reaction–diffusion system. Moreover, we compare our results with those of equilibrium solutions to demonstrate the differences between Turing instability of the equilibrium solutions and the periodic solutions.