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Zbl 1231.37054
Xiao, Hai-Bin
Global analysis of Ivlev's type predator-prey dynamic systems. (English)
[J] Appl. Math. Mech., Engl. Ed. 28, No. 4, 461-470 (2007). ISSN 0253-4827; ISSN 1573-2754/e

Summary: 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.

MSC 2000:: *37N25 Dynamical systems in biology
92B05 General biology and biomathematics

Keywords: limit cycle; global stability; Ivlev's type functional response; density restrict; existence and uniqueness

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