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http://dx.doi.org/10.4134/JKMS.j190036

BIFURCATION ANALYSIS OF A SINGLE SPECIES REACTION-DIFFUSION MODEL WITH NONLOCAL DELAY  

Zhou, Jun (School of Mathematics and Statistics Southwest University)
Publication Information
Journal of the Korean Mathematical Society / v.57, no.1, 2020 , pp. 249-281 More about this Journal
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;
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