Bifurcation analysis of a single species reaction-diffusion model with nonlocal delay
J. Korean Math. Soc. 2020 Vol. 57, No. 1, 249-281
https://doi.org/10.4134/JKMS.j190036
Published online January 1, 2020
Jun Zhou
Southwest University
Abstract : A reaction-diffusion model with spatiotemporal delay modeling the dynamical behavior of a single species is investigated. The parameter regions for the local stability, global stability and instability of the unique positive constant steady state solution are derived. The conditions of the occurrence of Turing (diffusion-driven) instability are obtained. The existence of time-periodic solutions, the existence and nonexistence of nonconstant positive steady state solutions are proved by bifurcation method and energy method. Numerical simulations are presented to verify and illustrate the theoretical results.
Keywords : Reaction-diffusion model, nonlocal delay, spatiotemporal patterns, turing instability, Hopf bifurcation, steady state bifurcation, nonconstant positive solutions
MSC numbers : Primary 35J55, 35K55, 92C15, 92C40
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