Complex dynamics of a Holling-type IV predator-prey model

In this paper, we focus on a spatial Holling-type IV predator-prey model which contains some important factors, such as diffusion, noise (random fluctuations) and external periodic forcing. By a brief stability and bifurcation analysis, we arrive at the Hopf and Turing bifurcation surface and derive...

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Bibliographic Details
Published in:arXiv.org 2008-01
Main Authors: Zhang, Lei, Wang, Weiming, Xue, Yakui, Jin, Zhen
Format: Article
Language:English
Subjects:
Bifurcations
Computer simulation
Mathematical models
Noise
Predator-prey simulation
Reaction-diffusion equations
Stability
Stability analysis
Variations
Online Access:Get full text
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Summary:In this paper, we focus on a spatial Holling-type IV predator-prey model which contains some important factors, such as diffusion, noise (random fluctuations) and external periodic forcing. By a brief stability and bifurcation analysis, we arrive at the Hopf and Turing bifurcation surface and derive the symbolic conditions for Hopf and Turing bifurcation in the spatial domain. Based on the stability and bifurcation analysis, we obtain spiral pattern formation via numerical simulation. Additionally, we study the model with colored noise and external periodic forcing. From the numerical results, we know that noise or external periodic forcing can induce instability and enhance the oscillation of the species, and resonant response. Our results show that modeling by reaction-diffusion equations is an appropriate tool for investigating fundamental mechanisms of complex spatiotemporal dynamics.
ISSN:2331-8422