Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 09, pp. 1-16.

Title: Stability and Hopf bifurcation in a symmetric
       Lotka-Volterra predator-prey system with delays
        
Authors: Jing Xia   (Peking Univ., Beijing, China)
         Zhixian Yu (Univ. of Shanghai for Science and Tech, China)
         Rong Yuan  (Beijing Normal Univ., Beijing, China)

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.


Submitted September 28, 2012. Published January 09, 2013.
Math Subject Classifications: 34K18, 37G05, 37G10, 92D25.
Key Words: Predator-prey system; delay; stability;
           Hopf bifurcation; normal form.