Bifurcation and Chaos control of Van der pol system with delay

The dynamic characteristics of the Van der pol system with delay are investigated in this paper. By substituting variables, the characteristic equations are obtained. The stability of trivial equilibrium is discussed by analyzing distribution of the roots of the characteristic equations. If the system is instable on the equilibrium points, the roots of the characteristic equations should meet the equation Re (λ) =0, from which, the result of to is got and the critical values of delay is found. It is found that Hopf bifurcation occurs from trivial equilibrium when the delay passes through critical values, then the critical values and their relations with system parameters are obtained. By adding delays to change the motion of the forced vibration of Van der pol system, and by numerical simulation, we got the time-delay system´s bifurcation diagram.