Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 72, Issue 1, Pages 147-177Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2016.04.049
Keywords
Reaction-diffusion; Lotka-Volterra model; Lyapunov-Schmidt reduction; Hopf bifurcation; Stability
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Funding
- National Natural Science Foundation of P.R. China [11271115]
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In this paper, we investigate the dynamics of a class of diffusive Lotka-Volterra equation with time delay subject to the homogeneous Dirichlet boundary condition in a bounded domain. The existence of spatially nonhomogeneous steady state solution is investigated by applying Lyapunov-Schmidt reduction. The stability and nonexistence of Hopf bifurcation at the spatially nonhomogeneous steady-state solution with the changes of a specific parameter are obtained by analyzing the distribution of the eigenvalues. Moreover, we illustrate our general results by applications to models with a single delay and one-dimensional spatial domain. (C) 2016 Elsevier Ltd. All rights reserved.
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