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

Wenjie Zuo | Zendy

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

Author(s) -

Wenjie Zuo

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/592547

Subject(s) - neumann boundary condition , mathematics , constant (computer programming) , bifurcation , instability , stability (learning theory) , hopf bifurcation , mathematical analysis , homogeneous , steady state (chemistry) , turing , boundary value problem , nonlinear system , physics , mechanics , computer science , quantum mechanics , machine learning , combinatorics , programming language , chemistry

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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