Journal of Applied Mathematics

Global Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage Structure

Lingshu Wang and Guanghui Feng

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Abstract

A delayed predator-prey system with Holling type II functional response and stage structure for both the predator and the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By means of persistence theory on infinite dimensional systems, it is proved that the system is permanent. By using Lyapunov functions and the LaSalle invariant principle, the global stability of each of the feasible equilibria of the model is discussed. Numerical simulations are carried out to illustrate the main theoretical results.

Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 431671, 10 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305554

Digital Object Identifier
doi:10.1155/2014/431671

Mathematical Reviews number (MathSciNet)
MR3176819

Zentralblatt MATH identifier
07010632

Citation

Wang, Lingshu; Feng, Guanghui. Global Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage Structure. J. Appl. Math. 2014 (2014), Article ID 431671, 10 pages. doi:10.1155/2014/431671. https://projecteuclid.org/euclid.jam/1425305554


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