The numerical Hopf bifurcation for Price Reyleigh equation with two delays was investigated

through using a delay as a parameter.First

the delay difference equation obtained by using Euler method was written as a map.And then according to the theories of bifurcation for discrete dynamical systems

on condition that Price Reyleigh equation had bifurcations

the conditions of Hopf bifurcation difference equations as well as the relations between successive system and numerical approximation were discussed.Finally

it is proved that when successive system produces Hopf bifurcation

the Euler discretion produces a Neimark-Sacker bifurcation.Further

it draws the conclusion that the Euler discretion preserves the features of the Hopf bifurcation.