Auto-oscillation of a generalized Gause type model with a convex contraint

Abstract

In this paper, we study the generalized Gause model in which the functional and numerical responses of the predators need not be monotonic functions and the intrinsic mortality rate of the predators is a variable function. As a result, we have established sufficient conditions for the existence, uniqueness and global stability of limit cycles confined in a closed convex nonempty set, by relying on a recent Lobanova and Sadovskii theorem. Moreover, we prove sufficient conditions for the existence of Hopf bifurcation. Eventually using scilab, we illustrate the validity of the results with numerical simulations.