Small-amplitude limit cycles of some Liénard-type systems

As we know, the Liénard system and its generalized forms are classical and important models of nonlinear oscillators, and have been widely studied by mathematicians and scientists. The main problem considered by most people is the number of limit cycles. In this paper, we investigate two kinds of Liénard systems and obtain the maximal number (i.e. the least upper bound) of limit cycles appearing in Hopf bifurcations by applying some known bifurcation theorems with technical analysis.