Criteria on the existence of limit cycles in planar polynomial differential systems
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Date
2022
Authors
Giné, Jaume
Grau Montaña, Maite
Llibre, Jaume
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Abstract
We summarize known criteria for the non-existence, existence and on the number of limit
cycles of autonomous real planar polynomial differential systems, and also provide new results.
We give examples of systems which realize the maximum number of limit cycles provided
by each criterion. In particular we consider the class of differential systems of the form ̇x =
Pn (x, y) + Pm (x, y), ̇y = Qn (x, y) + Qm (x, y), where n, m are natural numbers with m > n ≥ 1
and (Pi , Qi ) for i = n, m, are quasi-homogeneous vector fields.
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Expositiones Mathematicae, 2022, vol. 40, núm. 4, p. 1049-1083