Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 250, Issue 6, Pages 2779-2806Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2011.01.011
Keywords
Reaction-diffusion system; Spatially nonhomogeneous steady-state solution; Diffusion delay; Hopf bifurcation
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Funding
- Natural Science and Engineering Research Council of Canada
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We consider a reaction-diffusion system with general time-delayed growth rate and kernel functions. The existence and stability of the positive spatially nonhomogeneous steady-state solution are obtained. Moreover, taking minimal time delay tau as the bifurcation parameter, Hopf bifurcation near the steady-state solution is proved to occur at a critical value tau = tau(0). Especially, the Hopf bifurcation is forward and the bifurcated periodic solutions are stable on the center manifold. The general results are applied to competitive and cooperative systems with weak or strong kernel function respectively. (C) 2011 Elsevier Inc. All rights reserved.
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