Abstract
© 2016 Elsevier Inc. 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.
Original language | English |
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Pages (from-to) | 572-579 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 449 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 May 2017 |
Keywords
- Averaging theory
- Cyclicity
- Limit cycle
- Piecewise smooth vector fields