In this paper,on the basis of the theories and methods of ecology and ordinary differential equations,an ecological model with an impulsive control strategy is established.By using the theories of impulsive equations,...In this paper,on the basis of the theories and methods of ecology and ordinary differential equations,an ecological model with an impulsive control strategy is established.By using the theories of impulsive equations,small amplitude perturbation skills and compar-ison technique,we get the condition which guarantees the global asymptotical stability of the prey-x-eradication and predator-y-eradication periodic solution.It is proved that the system is permanent.Furthermore,numerical simulations are also illustrated which agree well with our theoretical analysis.All these results may be useful in study of the dynamic complexity of ecosystems.展开更多
In this paper, we derive a time-delayed and diffusive echinococcosis transmission model. We first address the well-posedness to the initial-value problem for the model and give the basic reproduction number TO0. In th...In this paper, we derive a time-delayed and diffusive echinococcosis transmission model. We first address the well-posedness to the initial-value problem for the model and give the basic reproduction number TO0. In the case of a bounded spatial domain, we establish the local stability as well as the global stability of the disease-free and disease equilibria of the model. The methods to prove the local and the global stability are to analyze the corresponding characteristic equations and construct Lyapunov functionals, respectively. In the case of an unbounded spatial domain, by applying Schauder＇s fixed point theorem and the limiting arguments, we show that when R0 〉 1, there exists a constant c＊ 〉 0 such that the model admits positive traveling wave solutions connecting the disease-free and endemic equilibrium for c 〉 c＊, and when R0 〉 1 and c 〈 c＊, the model has no positive traveling wave solutions connecting them.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No.60804015)National Basic Research Program of China (Grant No.2010CB732501)
文摘In this paper,on the basis of the theories and methods of ecology and ordinary differential equations,an ecological model with an impulsive control strategy is established.By using the theories of impulsive equations,small amplitude perturbation skills and compar-ison technique,we get the condition which guarantees the global asymptotical stability of the prey-x-eradication and predator-y-eradication periodic solution.It is proved that the system is permanent.Furthermore,numerical simulations are also illustrated which agree well with our theoretical analysis.All these results may be useful in study of the dynamic complexity of ecosystems.
文摘In this paper, we derive a time-delayed and diffusive echinococcosis transmission model. We first address the well-posedness to the initial-value problem for the model and give the basic reproduction number TO0. In the case of a bounded spatial domain, we establish the local stability as well as the global stability of the disease-free and disease equilibria of the model. The methods to prove the local and the global stability are to analyze the corresponding characteristic equations and construct Lyapunov functionals, respectively. In the case of an unbounded spatial domain, by applying Schauder＇s fixed point theorem and the limiting arguments, we show that when R0 〉 1, there exists a constant c＊ 〉 0 such that the model admits positive traveling wave solutions connecting the disease-free and endemic equilibrium for c 〉 c＊, and when R0 〉 1 and c 〈 c＊, the model has no positive traveling wave solutions connecting them.
