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.
Citation
Wenjie Zuo. "Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System." Abstr. Appl. Anal. 2013 1 - 10, 2013. https://doi.org/10.1155/2013/592547