A Class Of Delay Lotka-volterra System, Hopf Bifurcation And Chaos Control

In the recent several decades, the bifurcation theory was applied in the biological systems more and more frequently, especially the Hopf bifurcation theory and Hassard theory, which is very important to ascertain whether a certain biological system with delay has periodic orbit and how to determine the stability and the direction of the bifurcation periodic solution.In this paper, a Lotka-Volterra system with time delay is studied by using the theory of functional equation and Hopf bifurcation, the condition on which positive equilibrium exists and the quality of Hopf bifurcation are given. Finally, we give sev-eral numerical simulations, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable state or a stable periodic orbit.