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ON THE CENTRE-FOCUS PROBLEM IN SOME LIÉNARD SYSTEMS
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ON THE CENTRE-FOCUS PROBLEM IN SOME LIÉNARD SYSTEMS
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Journal Article
ON THE CENTRE-FOCUS PROBLEM IN SOME LIÉNARD SYSTEMS
2017
Overview
A large family of planar systems of ODEs arising from Liénard equations is considered. A Liénard equation (ProQuest: ... denotes formula omitted.) is 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 x′ = y - F(x), y′ = -g(x), where F′(x) = f(x). In this paper f(x) = 2α2x + 3α3x2 + 4α4x3 and g(x) = c1x + c3x3 + c5x5 + c7x7. In the parameter space (α2,α3,α4,c1,c3,c5,c7) ∈ R7 we consider the center-focus problem and find necessary conditions for the corresponding system having a center at the origin. In the parameter space (α2,α3,α4,c1,c3,c5,c7) ∈ R7 an example with a possible limit cycle and some examples with other complex dynamic behavior are presented.
Publisher
Univerza v Mariboru, Fakulteta za Energetiko
Subject
