In this paper, a model of Beddington-DeAngelies chemostat involving two species of micro-organism competing for two perfectly complementary growth-limiting nutrients and pulsed input of toxicant in the polluted enviro...In this paper, a model of Beddington-DeAngelies chemostat involving two species of micro-organism competing for two perfectly complementary growth-limiting nutrients and pulsed input of toxicant in the polluted environment was studied. Using Floquet theory and small amplitude perturbation method, a conclusion was that there exists twomicro-organism eradication periodic solution and which is global asymptotical stability. At the same time, the condition of the permanence for system was obtained. From the biological point of view, the method for protecting species is to improve the amount of impulsive period, and control the amount of toxicant input to the chemostat. Finally, our results are illustrated by numerical simulations.展开更多
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Acknowledgment This work is supported by Natural Science Foundation of Shanxi Province （2013011002-2）.
文摘In this paper, a model of Beddington-DeAngelies chemostat involving two species of micro-organism competing for two perfectly complementary growth-limiting nutrients and pulsed input of toxicant in the polluted environment was studied. Using Floquet theory and small amplitude perturbation method, a conclusion was that there exists twomicro-organism eradication periodic solution and which is global asymptotical stability. At the same time, the condition of the permanence for system was obtained. From the biological point of view, the method for protecting species is to improve the amount of impulsive period, and control the amount of toxicant input to the chemostat. Finally, our results are illustrated by numerical simulations.
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.
