Stability and Hopf bifurcation in a symmetric Lotka-Volterra predator-prey system with delays

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.

Keywords

• Predator-prey system
• delay
• stability
• Hopf bifurcation
• normal form