Medium Amplitude Limit Cycles of Some Classes of Generalized Liénard Systems

Abstract

We will consider two special families of polynomial perturbations of the linear center. For the resulting perturbed systems, which are generalized Liénard systems, we provide the exact upper bound for the number of limit cycles that bifurcate from the periodic orbits of the linear center.

Phase portraits of the quadratic polynomial Liénard differential systems

“…The polynomial Liénard differential systems and their applications also have been analysed by many authors these recent years. Thus some authors studied their limit cycles (see for instance [14,15,17,21,26,27,39,41]), or their algebraic limit cycles (see [28,31,37]), or their invariant algebraic curves (see [7,8,49]), or their canard limit cycles (see [43]), or the shape of their limit cycles (see [46]), or the period function of their centres (see [47]), or their integrability (see [9,30]), or a kind of a generalized Liénard system (see [18]).…”