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.