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Applied Mathematics and Mechanics

, Volume 28, Issue 4, pp 461–470 | Cite as

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

  • Xiao Hai-bin  (肖海滨)
Article

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.

Key words

limit cycle global stability Ivlev’s type functional response density restrict existence and uniqueness 

Chinese Library Classification

O175.15 

2000 Mathematics Subject Classification

37N25 92B05 

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References

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Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  1. 1.Department of MathematicsNingbo UniversityNingboP. R. China
  2. 2.Department of MathematicsNanjing UniversityNanjingP. R. China

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