Abstract:

Using the continuation theorem based on coincidence degree theory, we studied the existence of positive periodic solutions for a Lotka-Volteraa facultative mutualism system of three species with several delays. One bounded open set and a set of sufficient conditions for this system to have at least one positive periodic solution were obtained by using analytic technique. It was revealed that when the facultative mutualism coefficient and density dependence coefficient of three species are under certain conditions, the system will bring periodic oscillation of biological nature.

Key words: facultative mutualism system, positive periodic solution, several delays, coincidence degree theory