A strongly coupled predator-prey system with modified Holling-Tanner functional response

In this paper, a strongly coupled system of partial differential equations in a bounded domain with the homogeneous Neumann boundary condition which models a predator-prey system with modified Holling-Tanner functional response is considered. First, the authors study the stability of the positive constant solution. Sufficient conditions are derived for the global stability of the positive equilibrium by constructing a suitable Lyapunov function. By using the Leray-Schauder theorem, the authors prove a number of existence and non-existence results about the non-constant steady states of the system. (C) 2010 Elsevier Ltd. All rights reserved.