Non-permanence for three-species Lotka-Volterra cooperative difference systems

Abstract

Abstract The permanence for three-species cooperative difference systems of Lotka-Volterra is considered. By constructing some suitable regions, we prove that a cooperative system cannot be permanent. Furthermore, we find the orbits starting from our regions approach the coordinate axes as n tends to infinity. This is somewhat similar to the May-Leonard behavior in the case of competition models.

Keywords

• Lotka-Volterra system
• cooperative
• difference system
• permanence