Abstract and Applied Analysis

Spatially Nonhomogeneous Periodic Solutions in a Delayed Predator-Prey Model with Diffusion Effects

Jia-Fang Zhang

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Abstract

This paper is concerned with a delayed predator-prey diffusion model with Neumann boundary conditions. We study the asymptotic stability of the positive constant steady state and the conditions for the existence of Hopf bifurcation. In particular, we show that large diffusivity has no effect on the Hopf bifurcation, while small diffusivity can lead to the fact that spatially nonhomogeneous periodic solutions bifurcate from the positive constant steady-state solution when the system parameters are all spatially homogeneous. Meanwhile, we study the properties of the spatially nonhomogeneous periodic solutions applying normal form theory of partial functional differential equations (PFDEs).

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 856725, 21 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1355495786

Digital Object Identifier
doi:10.1155/2012/856725

Mathematical Reviews number (MathSciNet)
MR2947768

Zentralblatt MATH identifier
1246.34041

Citation

Zhang, Jia-Fang. Spatially Nonhomogeneous Periodic Solutions in a Delayed Predator-Prey Model with Diffusion Effects. Abstr. Appl. Anal. 2012 (2012), Article ID 856725, 21 pages. doi:10.1155/2012/856725. https://projecteuclid.org/euclid.aaa/1355495786


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