Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System

Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System

The dynamics of a diffusive ratio-dependent Holling-Tanner predator-prey system subject to Neumann boundary conditions are considered. By choosing the ratio of intrinsic growth rates of predators to preys as a bifurcation parameter, the existence and stability of spatially homogeneous and nonhomogen...

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Main Author: Wenjie Zuo
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/592547
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spelling doaj-74e0635b683b43e0b1e72d0ed5ea3b442020-11-24T22:26:36ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/592547592547Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner SystemWenjie Zuo0College of Science, China University of Petroleum (East China), Qingdao, Shandong 266580, ChinaThe dynamics of a diffusive ratio-dependent Holling-Tanner predator-prey system subject to Neumann boundary conditions are considered. By choosing the ratio of intrinsic growth rates of predators to preys as a bifurcation parameter, the existence and stability of spatially homogeneous and nonhomogeneous Hopf bifurcations and steady state bifurcation are investigated in detail. Meanwhile, we show that Turing instability takes place at a certain critical value; that is, the stationary solution becomes unstable induced by diffusion. Particularly, the sufficient conditions of the global stability of the positive constant coexistence are given by the upper-lower solutions method.http://dx.doi.org/10.1155/2013/592547
collection DOAJ
language English
format Article
sources DOAJ
author Wenjie Zuo
spellingShingle Wenjie Zuo
Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System
Abstract and Applied Analysis
author_facet Wenjie Zuo
author_sort Wenjie Zuo
title Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System
title_short Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System
title_full Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System
title_fullStr Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System
title_full_unstemmed Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System
title_sort global stability and bifurcations of a diffusive ratio-dependent holling-tanner system
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description The dynamics of a diffusive ratio-dependent Holling-Tanner predator-prey system subject to Neumann boundary conditions are considered. By choosing the ratio of intrinsic growth rates of predators to preys as a bifurcation parameter, the existence and stability of spatially homogeneous and nonhomogeneous Hopf bifurcations and steady state bifurcation are investigated in detail. Meanwhile, we show that Turing instability takes place at a certain critical value; that is, the stationary solution becomes unstable induced by diffusion. Particularly, the sufficient conditions of the global stability of the positive constant coexistence are given by the upper-lower solutions method.
url http://dx.doi.org/10.1155/2013/592547
work_keys_str_mv AT wenjiezuo globalstabilityandbifurcationsofadiffusiveratiodependenthollingtannersystem
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