An upper bound for the number of small-amplitude limit cycles in non-smooth Liénard system

Abstract

The non-smooth Liénard system, a well-known nonlinear model, appears in a natural way in physics, chemistry, biology, and so on, in which periodic phenomena play a relevant role. In this paper, we investigate the small-amplitude limit cycles generated by the Hopf bifurcation of the non-smooth Liénard system. By utilizing the Picard–Fuchs equation, we gain the upper bounds of the number of small-amplitude limit cycles for a generic non-smooth Liénard system. Finally, an example is given to illustrate the efficiency of the theoretical results.