Hopf Bifurcation in Numerical Approximation for Price Reyleigh Equation with Finite Delay

The numerical approximation of Price Reyleigh equation is considered using delay as parameter. Fist, the delay difference equation obtained by using Euler method is written as a map.According to the theories of bifurcation for discrete dynamical systems, the conditions to guarantee the existence of Hopf bifurcation for numerical approximation are given. The relations of Hopf bifurcation between the continuous and the discrete are discussed. That when the Price Reyleigh equation has Hopf bifurcations at , the numerical approximation also has Hopf bifurcations at is proved.