The Limit Cycle Bifurcation Of LIENARD System And Averaging Method

In this article we first recall the maximum number of limit cycles of the polynomial Lienard differential systems bifurcating from a rest point obtained by using the averaging method of first, second and third order by Professor Llibre. Next we provide the calculation formula of the averaging method of fourth order with a proof of this formula. Finally, we apply the averaging method of fourth order to compute the maximum number, denoted by ( )H 4 m, n , of limit cycles of the polynomial Lienard differential systems which are bifurcated from one rest point of the systems.