Turing–Hopf Bifurcation Analysis of the Sel’kov–Schnakenberg System

Author:

Liu Yuying1ORCID,Wei Xin2ORCID

Affiliation:

1. School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, P. R. China

2. School of Mathematical Sciences, Heilongjiang University, Harbin, Heilongjiang 150001, P. R. China

Abstract

In this paper, we investigate the spatiotemporal dynamics of the Sel’kov–Schnakenberg system. The stability of the positive constant steady state is studied by the linear stability theory. Hopf bifurcation and Turing–Hopf bifurcation are generated by varying two parameters in the model. The normal form near the Turing–Hopf singularity is calculated to explore the complex dynamics of the system. Finally, numerical simulations are carried out to verify the theoretical results. Our results show that the Sel’kov–Schnakenberg system exhibits complex dynamics near the Turing–Hopf singularity, including the existence of inhomogeneous steady states, homogeneous periodic solutions and inhomogeneous periodic solutions.

Funder

National Natural Science Foundation of China

Heilongjiang Provincial Natural Science Foundation of China

Natural Science Foundation of Jiangsu Province

Fundamental Research Funds for the Universities in Heilongjiang Province

Fundamental Research Funds for the Central Universities

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

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