## Journal of Applied Mathematics

### Stability Analysis of a Ratio-Dependent Predator-Prey Model Incorporating a Prey Refuge

#### Abstract

A ratio-dependent predator-prey model incorporating a prey refuge with disease in the prey population is formulated and analyzed. The effects of time delay due to the gestation of the predator and stage structure for the predator on the dynamics of the system are concerned. By analyzing the corresponding characteristic equations, the local stability of a predator-extinction equilibrium and a coexistence equilibrium of the system is discussed, respectively. Further, it is proved that the system undergoes a Hopf bifurcation at the coexistence equilibrium, when $\tau ={\tau }_{0}$. By comparison arguments, sufficient conditions are obtained for the global stability of the predator-extinction equilibrium. By using an iteration technique, sufficient conditions are derived for the global attractivity of the coexistence equilibrium of the proposed system.

#### Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 978758, 10 pages.

Dates
First available in Project Euclid: 2 March 2015

https://projecteuclid.org/euclid.jam/1425305624

Digital Object Identifier
doi:10.1155/2014/978758

Mathematical Reviews number (MathSciNet)
MR3191142

Zentralblatt MATH identifier
07010815

#### Citation

Wang, Lingshu; Feng, Guanghui. Stability Analysis of a Ratio-Dependent Predator-Prey Model Incorporating a Prey Refuge. J. Appl. Math. 2014 (2014), Article ID 978758, 10 pages. doi:10.1155/2014/978758. https://projecteuclid.org/euclid.jam/1425305624

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