Global Analysis of Ivlev’s Type Predator-Prey Dynamical System

A class of Ivlev. s type predator-prey dynamic systems with prey and predator both having linear density restricts is considered. By using the qualitative methods of ODE, the positive equilibrium's global stability and existence and uniqueness of non-small amplitude stable limit cycle were obtained. Especially under certain conditions, it shows that existence and uniqueness of non-small amplitude stable limit cycle is equivalent to the positive equilibrium's local unstability and the positive equilibrium's local stability 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.