Global dynamics of a cooperative discrete system in the plane

Abstract

In this paper, we consider the cooperative system x(n+1) = ax(n) + by(n)(2)/1 + y(n)(2), y(n+1) = cx(n)(2)/1 + x(n)(2) + dy(n), n = 0, 1, ... , where all parameters a, b, c, d are positive numbers and the initial conditions x(0), y(0) are non-negative numbers. We describe the global dynamics of this system in a number of cases. An interesting feature of this system is that it exhibits a coexistence of locally stable equilibrium and locally stable periodic solutions as well as the Allee effect.