Stability of Certain Non-Autonomous Cooperative Systems of Difference Equations with the Application to Evolutionary Dynamics

Abstract

This paper investigates the dynamics of non-autonomous cooperative systems of difference equations with asymptotically constant coefficients. We are mainly interested in global attractivity results for such systems and the application of such results to evolutionary population cooperation models. We use two methods to extend the global attractivity results for autonomous cooperative systems to related non-autonomous cooperative systems which appear in recent problems in evolutionary dynamics.

Keywords

• cooperative
• difference equations
• discrete dynamical systems
• evolutionary dynamics
• non-autonomous systems
• stability