Limit cycles of discontinuous piecewise polynomial vector fields

de Carvalho, Tiago [UNESP]; Llibre, Jaume; Tonon, Durval José

Limit cycles of discontinuous piecewise polynomial vector fields

Data

2017-05-01

Autores

de Carvalho, Tiago

Llibre, Jaume

Tonon, Durval José

Tipo

Artigo

Direito de acesso

Acesso restrito

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.