Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2013, Special Issue (2013), Article ID 168340, 13 pages.
The Hopf Bifurcation for a Predator-Prey System with -Logistic Growth and Prey Refuge
The Hopf bifurcation for a predator-prey system with -logistic growth and prey refuge is studied. It is shown that the ODEs undergo a Hopf bifurcation at the positive equilibrium when the prey refuge rate or the index- passed through some critical values. Time delay could be considered as a bifurcation parameter for DDEs, and using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results.
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 168340, 13 pages.
First available in Project Euclid: 26 February 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Wang, Shaoli; Ge, Zhihao. The Hopf Bifurcation for a Predator-Prey System with $\theta $ -Logistic Growth and Prey Refuge. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 168340, 13 pages. doi:10.1155/2013/168340. https://projecteuclid.org/euclid.aaa/1393449393