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

XIAO Hai-bin

Volume 28 Issue 4

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Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(4): 419-427

XIAO Hai-bin. Global Analysis of Ivlev’s Type Predator-Prey Dynamical System[J]. Applied Mathematics and Mechanics, 2007, 28(4): 419-427.

Citation:

XIAO Hai-bin. Global Analysis of Ivlev’s Type Predator-Prey Dynamical System[J]. Applied Mathematics and Mechanics, 2007, 28(4): 419-427.

Citation:

XIAO Hai-bin. Global Analysis of Ivlev’s Type Predator-Prey Dynamical System[J]. Applied Mathematics and Mechanics, 2007, 28(4): 419-427.

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

XIAO Hai-bin^1,2

1.
Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, P. R. China;

Received Date: 2006-05-12
Rev Recd Date: 2007-01-27
Publish Date: 2007-04-15

Abstract

Abstract

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.
- limit cycle,
- global stability,
- density restrict,
- Ivlev type functional response,
- existence and uniqueness

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References(4)

References

[1]	Sugie Jitsuro.Two-parameter bifurcation in a predator-prey system of Ivelv type[J].Journal of Mathematical Analysis and Application，1998,217(2):349-371. doi: 10.1006/jmaa.1997.5700
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