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- Title
STABILITY AND HOPF BIFURCATION IN A SYMMETRIC LOTKA-VOLTERRA PREDATOR-PREY SYSTEM WITH DELAYS.
- Authors
JING XIA; ZHIXIAN YU; RONG YUAN
- Abstract
This article concerns a symmetrical Lotka-Volterra predator-prey system with delays. By analyzing the associated characteristic equation of the original system at the positive equilibrium and choosing the delay as the bifurcation parameter, the local stability and Hopf bifurcation of the system are investigated. Using the normal form theory, we also establish the direction and stability of the Hopf bifurcation. Numerical simulations suggest an existence of Hopf bifurcation near a critical value of time delay.
- Subjects
LOTKA-Volterra equations; BIFURCATION theory; EQUILIBRIUM; DIFFERENTIAL equations; MATHEMATICAL models; MATHEMATICAL analysis
- Publication
Electronic Journal of Differential Equations, 2013, Vol 2013, p1
- ISSN
1550-6150
- Publication type
Article