Abstract and Applied Analysis

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

Wenjie Zuo

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 592547, 10 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512021

Digital Object Identifier
doi:10.1155/2013/592547

Mathematical Reviews number (MathSciNet)
MR3096815

Citation

Zuo, Wenjie. Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System. Abstr. Appl. Anal. 2013 (2013), Article ID 592547, 10 pages. doi:10.1155/2013/592547. https://projecteuclid.org/euclid.aaa/1393512021


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