Limit cycle bifurcations of some Liénard systems with a cuspidal loop and a homoclinic loop

In this paper, we study the number of limit cycles of some polynomial Liénard systems with a cuspidal loop and a homoclinic loop, and obtain some new results on the lower bound of the maximal number of limit cycles for these systems.

► We study some polynomial Lienard systems with a cuspidal loop and a homoclinic loop. ► We obtain the lower bound of the maximal number of limit cycles. ► Some of our results are new.