Consider a class of Ivlev＇s type predator-prey dynamic systems with prey and predator both having linear density restricts. By using the qualitative methods of ODE, the global stability of positive equilibrium and ex...Consider a class of Ivlev＇s type predator-prey dynamic systems with prey and predator both having linear density restricts. By using the qualitative methods of ODE, the global stability of positive equilibrium and existence and uniqueness of non-small amplitude stable limit cycle are obtained. Especially under certain conditions, it shows that existence and uniqueness of non-small amplitude stable limit cycle is equivalent to the local un-stability of positive equilibrium and the local stability of positive equilibrium implies its global stability. That is to say, the global dynamic of the system is entirely determined by the local stability of the positive equilibrium.展开更多
In this paper, we consider a nonautonomous multispecies competition-predator system with Holling＇s type Ⅲ functional response. The coexistence of the system, under some conditions, is obtained. Furthermore, using Ly...In this paper, we consider a nonautonomous multispecies competition-predator system with Holling＇s type Ⅲ functional response. The coexistence of the system, under some conditions, is obtained. Furthermore, using Lyapunov function, we show that the system has a strictly positive almost periodic solution which is globally asymptotically stable.展开更多
文摘Consider a class of Ivlev＇s type predator-prey dynamic systems with prey and predator both having linear density restricts. By using the qualitative methods of ODE, the global stability of positive equilibrium and existence and uniqueness of non-small amplitude stable limit cycle are obtained. Especially under certain conditions, it shows that existence and uniqueness of non-small amplitude stable limit cycle is equivalent to the local un-stability of positive equilibrium and the local stability of positive equilibrium implies its global stability. That is to say, the global dynamic of the system is entirely determined by the local stability of the positive equilibrium.
基金Project supported by the National Natural Science Foundation of China (No.10171010) the Key Project on Science and Technology of the Education Ministry of People's Republic of China (No. Key 01061).
文摘In this paper, we consider a nonautonomous multispecies competition-predator system with Holling＇s type Ⅲ functional response. The coexistence of the system, under some conditions, is obtained. Furthermore, using Lyapunov function, we show that the system has a strictly positive almost periodic solution which is globally asymptotically stable.
