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

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  • Wenjie Zuo

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.

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  • Wenjie Zuo, 2013. "Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, September.
    • Handle: RePEc:hin:jnlaaa:592547
    DOI: 10.1155/2013/592547
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