Pattern formation in a general Degn-Harrison reaction model
Bull. Korean Math. Soc. 2017 Vol. 54, No. 2, 655-666
Published online January 4, 2017
Printed March 31, 2017
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
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