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Global analysis of Ivlev’s type predator-prey dynamic systems

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Abstract

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.

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Correspondence to Xiao Hai-bin Doctor  (肖海滨).

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Communicated by LI Ji-bin

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Xiao, Hb. Global analysis of Ivlev’s type predator-prey dynamic systems. Appl Math Mech 28, 461–470 (2007). https://doi.org/10.1007/s10483-007-0406-1

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  • DOI: https://doi.org/10.1007/s10483-007-0406-1

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Chinese Library Classification

2000 Mathematics Subject Classification

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