ON THE CENTRE-FOCUS PROBLEM IN SOME LIÉNARD SYSTEMS - Mencinger, Matej (Journal of Energy Technology, 2024)
A large family of planar systems of ODEs arising from Liénard equations is considered. A Liénard equation ݂ commonly used in practical problems, in particular in(electro)mechanics. It is well‐known that a Liénard equation can be transformed into an autonomous planar system of ODEs of the form where In this paper݂ . In the parameter space we consider the center‐focus problem andfind necessary conditions for the corresponding system having a center at the origin. In the parameter space ܽ an example with a possible limit cycle and some examples with other complex dynamic behavior are presented.