Higher order Melnikov analysis for planar piecewise linear vector fields with nonlinear switching curve

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:287

Article

Andrade, Kamila da S.¹  Cespedes, Oscar A. R.²  Cruz, Dayane R.³  Novaes, Douglas D.³ 

[1] Univ Fed Goias, Inst Matemat & Estat, Campus 2, BR-74001970 Goiania, Go, Brazil

[2] Univ Fed Vicosa, Dept Matemat, Campus Univ, BR-36570000 Vicosa, MG, Brazil

[3] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, Dept Matemat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP, Brazil

关键词: Filippov systems;    Nonlinear switching manifold;    Piecewise linear differential systems;    Melnikov theory;    Periodic solutions;   

DOI  :  10.1016/j.jde.2021.03.039

来源: Elsevier

【 摘 要 】

In this paper, we are interested in providing lower estimations for the maximum number of limit cycles H(n) that planar piecewise linear differential systems with two zones separated by the curve y = xn can have, where n is a positive integer. For this, we perform a higher order Melnikov analysis for piecewise linear perturbations of the linear center. In particular, we obtain that H (2) >= 4, H (3) >= 8, H(n) >= 7, for n >= 4 even, and H(n) >= 9, for n >= 5 odd. This improves all the previous results for n >= 2. Our analysis is mainly based on some recent results about Chebyshev systems with positive accuracy and Melnikov Theory, which will be developed at any order for a class of nonsmooth differential systems with nonlinear switching manifold. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free