Limit cycles of discontinuous piecewise polynomial vector fields

作者：de Carvalho Tiago; Llibre Jaume; Tonon Durval Jose

来源：Journal of Mathematical Analysis and Applications, 2017, 449(1): 572-579.

DOI：10.1016/j.jmaa.2016.11.048

• Piecewise smooth vector fields
• Limit cycle
• Averaging theory
• Cyclicity

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) over dot = -y((x(2) + y(2))/2)(m) and (y) over dot = x((x(2) + y(2))/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.

• 出版日期2017-5-1