The number of medium amplitude limit cycles of some generalized Li\'enard systems

TL;DR

This paper establishes the maximum number of limit cycles that can emerge from certain generalized Li'enard systems under polynomial perturbations, advancing understanding of their bifurcation behavior.

Contribution

It provides the exact upper bound for the number of limit cycles bifurcating from the linear center in specific polynomial perturbations of generalized Li'enard systems.

Findings

Exact upper bound for bifurcating limit cycles

Limits on the number of limit cycles in perturbed systems

Enhanced understanding of bifurcation in Li'enard systems

Abstract

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