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Dynamics of mutualism-competition-predator system with Beddington-DeAngelis functional responses and impulsive perturbations. (English) Zbl 1253.92046

Summary: We explore the dynamics of a class of mutualism-competition-predator interaction models with Beddington-DeAngelis functional responses and impulsive perturbations. Sufficient conditions for existence of positive periodic solution are established by using a continuation theorem in coincidence degree theory, which have been extensively applied in studying existence problems in differential equations and difference equations. In addition, sufficient criteria are given for the global stability and the globally exponential stability of system by employing comparison principle and Lyapunov method.

MSC:

92D40 Ecology
34A37 Ordinary differential equations with impulses
37N25 Dynamical systems in biology
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