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

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

Author(s) -

JiaFang Zhang

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/856725

Subject(s) - mathematics , hopf bifurcation , neumann boundary condition , mathematical analysis , constant (computer programming) , steady state (chemistry) , bifurcation , boundary value problem , diffusion , homogeneous , thermal diffusivity , stability (learning theory) , partial differential equation , nonlinear system , thermodynamics , physics , chemistry , quantum mechanics , combinatorics , machine learning , computer science , programming language

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). Copyright © 2012 Jia-Fang Zhang.

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