ON THE CENTRE-FOCUS PROBLEM IN SOME LIÉNARD SYSTEMS
DOI:
https://doi.org/10.18690/jet.10.3.57-69.2017Keywords:
Polynomial system of ODEs, Center-focus problem, Complex behaviorAbstract
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 and
find 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.
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References
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