Maximum Number of Small Limit Cycles in Some Rational Liénard Systems with Cubic Restoring Terms.

In this paper, we obtain an upper bound for the number of small-amplitude limit cycles produced by Hopf bifurcation in one particular type of rational Liénard systems in the form of ẋ = y − q n (x) / p m (x) , ẏ = − g (x) , where q n (x) and p m (x) are polynomials in x with degrees n and m , respectively. Furthermore, we show that the upper bound presented here is sharp in the case of m = n. [ABSTRACT FROM AUTHOR]