Global analysis of Ivlev’s type predator-prey dynamic systems
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.
Key wordslimit cycle global stability Ivlev’s type functional response density restrict existence and uniqueness
Chinese Library ClassificationO175.15
2000 Mathematics Subject Classification37N25 92B05
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- Tang Qiulin. A Predator-prey System with Ivlev’s Functional Response[J]. Journal of Beihua University(Natural Science), 2002, 3(5):381–384 (in Chinese).Google Scholar