Existence and uniqueness of limit cycles in planar system of Liénard type

This paper is a study of one of the most beautiful phenomena in dynamical systems limit cycle. In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory having the property that at least one other trajectory spirals into it as time appro...

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Bibliographic Details
Published in:Rendiconti del Circolo matematico di Palermo 2018-12, Vol.67 (3), p.547-556
Main Authors: Kasbi, Tohid, Roomi, Vahid
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Chaos theory
Dynamical systems
Geometry
Mathematics
Mathematics and Statistics
Spirals
Trajectories
Uniqueness
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Summary:This paper is a study of one of the most beautiful phenomena in dynamical systems limit cycle. In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory having the property that at least one other trajectory spirals into it as time approaches either positive or negative infinity. In this paper, existence and uniqueness of limit cycles for a generalized Liénard system will be studied. Moreover, some examples will be presented to illustrate our results.
ISSN:0009-725X
1973-4409
DOI:10.1007/s12215-018-0333-2