Hopf Cyclicity of a Class of Liénard-Type Systems

Abstract

The Hopf cyclicities of some smooth polynomial, rational polynomial and piecewise smooth Liénard systems are studied. For two Liénard systems with the same damping term and different restoring (or potential) terms, we provide sufficient conditions that the two systems have the same Hopf cyclicity. Then, some examples are given to illustrate the efficiency and applicability of our results.