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.
Jun Zhou
Southwest University
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
2015; 52(4): 1113-1122
2013; 50(2): 353-373
1996; 33(2): 319-328
1996; 33(4): 631-638
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd