Electron. J. Diff. Equ., Vol. 2014 (2014), No. 192, pp. 1-15.

A density-dependent predator-prey model of Beddington-DeAngelis type

Haiyin Li, Zhikun She

Abstract:
In this article, we study the dynamics of a density-dependent predator-prey system of Beddington-DeAngelis type. We obtain sufficient and necessary conditions for the existence of a unique positive equilibrium, the global attractiveness of the boundary equilibrium, and the permanence of the system, respectively. Moreover, we derive a sufficient condition for the locally asymptotic stability of the positive equilibrium by the Lyapunov function theory and a sufficient condition for the global attractiveness of the positive equilibrium by the comparison theory.

Submitted November 16, 2013. Published September 16, 2014.
Math Subject Classifications: 34D23, 92D25.
Key Words: Density dependence; global attractiveness; omega-limit set; permanence.

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Haiyin Li
LMIB and School of Mathematics and Systems Science
Beihang University, Beijing, China
email: lihaiyin2013@163.com
Zhikun She
SKLSDE, LMIB and School of Mathematics and Systems Science
Beihang University, Beijing, China
email: zhikun.she@buaa.edu.cn

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