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

Wenjie Zuo

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

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.

Date: 2013
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https://doi.org/10.1155/2013/592547

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:592547

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