Bounding the number of limit cycles for parametric Lienard systems using symbolic computation methods

摘要

This paper presents a systematical and algorithmic approach for determining the maximum number of limit cycles of parametric Li & eacute;nard system that bifurcate from the period annulus of the corresponding Hamiltonian system. We provide an algebraic criterion for the Melnikov function of the considered system to have Chebyshev property. By using this criterion, we reduce the problem of analyzing the Chebyshev property to that of solving some (parametric) semi-algebraic systems, and a systematical approach with polynomial algebra methods to solve such semi-algebraic systems is explored. The feasibility of the proposed approach has been shown by several concrete Li & eacute;nard systems.(c) 2021 Elsevier B.V. All rights reserved.