Limit cycles of discontinuous piecewise polynomial vector fields
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Data
2017-05-01
Autores
de Carvalho, Tiago [UNESP]
Llibre, Jaume
Tonon, Durval José
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Resumo
When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x˙=−y((x2+y2)/2)m and y˙=x((x2+y2)/2)m with m≥1, when we perturb it inside a class of discontinuous piecewise polynomial vector fields of degree n with k pieces. The positive integers m, n and k are arbitrary. The main tool used for proving our results is the averaging theory for discontinuous piecewise vector fields.
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Averaging theory, Cyclicity, Limit cycle, Piecewise smooth vector fields
Como citar
Journal of Mathematical Analysis and Applications, v. 449, n. 1, p. 572-579, 2017.