Dynamics of a Predator-Prey Reaction-Diffusion System with Non-Monotonic Functional Response Function
Year: 2018
Author: Huan Wang, Cunhua Zhang
Annals of Applied Mathematics, Vol. 34 (2018), Iss. 2 : pp. 199–220
Abstract
In this article, a two-species predator-prey reaction-diffusion system with Holling type-IV functional response and subject to the homogeneous Neumann boundary condition is regarded. In the absence of the spatial diffusion, the local asymptotic stability, the instability and the existence of Hopf bifurcation of the positive equilibria of the corresponding local system are analyzed in detail by means of the basic theory for dynamical systems. As well, the effect of the spatial diffusion on the stability of the positive equilibria is considered by using the linearized method and analyzing in detail the distribution of roots in the complex plane of the associated eigenvalue problem. In order to verify the obtained theoretical predictions, some examples and numerical simulations are also included by applying the numerical methods to solve the ordinary and partial differential equations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2018-AAM-20573
Annals of Applied Mathematics, Vol. 34 (2018), Iss. 2 : pp. 199–220
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: reaction-diffusion system predator-prey system asymptotic stability Hopf bifurcation.