Stability of a general predator-prey model (Q2640025)

A general two species predator-prey system modelled by the differential equations \(dx/dt=\phi (x)(F(x)-\pi (y)),\) \(dy/dt=\rho (y)\psi (x),\) is considered qualitatively in the phase plane \({\mathbb{R}}^ 2\); x is the prey density, y is the predator density. Conditions for an interior equilibrium in \({\mathbb{R}}^ 2_+\) are given, and the local and global stability of this equilibrium is analyzed.