Hopf bifurcation and Turing instability in the reaction-diffusion Holling-Tanner predator-prey model

The reaction-diffusion Holling-Tanner predator-prey model with Neumann boundary condition is considered. We perform a detailed stability and Hopf bifurcation analysis and derive conditions for determining the direction of bifurcation and the stability of the bifurcating periodic solution. For partia...

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Bibliographic Details
Published inIMA journal of applied mathematics Vol. 78; no. 2; pp. 287 - 306
Main Authors Li, X., Jiang, W., Shi, J.
Format Journal Article
LanguageEnglish
Published 01.04.2013
Subjects
Bifurcations
Bistability
Differential equations
Hopf bifurcation
Instability
Mathematical models
Partial differential equations
Stability
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Summary:The reaction-diffusion Holling-Tanner predator-prey model with Neumann boundary condition is considered. We perform a detailed stability and Hopf bifurcation analysis and derive conditions for determining the direction of bifurcation and the stability of the bifurcating periodic solution. For partial differential equation (PDE), we consider the Turing instability of the equilibrium solutions and the bifurcating periodic solutions. Through both theoretical analysis and numerical simulations, we show the bistability of a stable equilibrium solution and a stable periodic solution for ordinary differential equation and the phenomenon that a periodic solution becomes Turing unstable for PDE.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxr050