• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.655-666
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• 2017

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.