Hopf Bifurcation For A Limited Time Delay Of The Generalized Li¨¦nard Equation

This article studies the stability and the Hopf bifurcation of zero solution of the generalized Lienard equationwith finite time delay,where b is bifurcated parameter ( the dcfination of b will be shown later). Firstly, we give the bifurcation diagram in the parameter plane (r,b), according to which we can give the stable and unstable regions of the equation's /oro solution and the Hopf bifurcated curve of Hopf bifurcation in the parameter plane (r,b) . Secondly, we show the calculating formulae about the quality of Hopf bifurcation in the first bifurcated curve with the normal form method of calculating Hopf bifurcation. Lastly, we apply the formulae about the quality of Ilopf bifurcation we have obtained to a concrete example, calculating the stability of periodic solution,the direction of Hopf bifurcation and the expression of bifurcated periodic solution.