On the Stability of Four Dimensional Lotka-Volterra Prey-Predator System

The aim of this work is to study a modified version the four-dimensional Lotka-Volterra model. In model, all four species grow logistically. This model has at most sixteen possible equilibrium points. Five them always exist without any restriction on parameters while existence other points subject fulfillment some necessary and sufficient conditions. Eight are unstable rest locally asymptotically stable under certain conditions, addition, basin attraction found for each point that can be stable. Conditions provided ensure solutions bounded. Finally, numerical simulations given verify support obtained theoretical results.