Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2017; 54(2): 655-666

Online first article January 4, 2017      Printed March 31, 2017

https://doi.org/10.4134/BKMS.b160249

Copyright © The Korean Mathematical Society.

Pattern formation in a general Degn-Harrison reaction model

Jun Zhou

Southwest University

Abstract

In this paper, we study the pattern formation to a general Degn-Harrison reaction model. We show Turing instability happens by analyzing the stability of the unique positive equilibrium with respect to the PDE model and the corresponding ODE model, which indicate the existence of the non-constant steady state solutions. We also show the existence periodic solutions of the PDE model and the ODE model by using Hopf bifurcation theory. Numerical simulations are presented to verify and illustrate the theoretical results.

Keywords: Degn-Harrison reaction model, pattern formation, Turing instability, Hopf bifurcation

MSC numbers: 35B36, 35B32, 35K57, 35J61, 92C40, 92C45, 92E20