In this paper, we present a diffusive predator prey system with Beddington-DeAngelis funetionM response, where the prey species can disperse between the two patches, and there is competition between the two predators....In this paper, we present a diffusive predator prey system with Beddington-DeAngelis funetionM response, where the prey species can disperse between the two patches, and there is competition between the two predators. Sufficient conditions for the permanence and extinction of system are established based on the upper and lower solution meth- ods and comparison theory of differential equation. Furthermore, the global asymptotic stability of positive solutions is obtained by constructing a suitable Lyapunov function. By using the continuation theorem in coincidence degree theory, we show the periodicity of positive solutions. Finally, we illustrate global asymptotic stability of the model by a simulation figure.展开更多
基金The authors are grateful to their classmates and teachers for comments and valuable suggestions. This work is supported by the National Natural Science Foundation of China （No. 70672103）.
文摘In this paper, we present a diffusive predator prey system with Beddington-DeAngelis funetionM response, where the prey species can disperse between the two patches, and there is competition between the two predators. Sufficient conditions for the permanence and extinction of system are established based on the upper and lower solution meth- ods and comparison theory of differential equation. Furthermore, the global asymptotic stability of positive solutions is obtained by constructing a suitable Lyapunov function. By using the continuation theorem in coincidence degree theory, we show the periodicity of positive solutions. Finally, we illustrate global asymptotic stability of the model by a simulation figure.
