NDLI: Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields

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Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields

Content Provider	Scilit
Author	Cardoso, João L. Llibre, Jaume Novaes, Douglas D. Tonon, Durval J.
Copyright Year	2020
Description	In the present study we consider planar piecewise linear vector fields with two zones separated by the straight line x=0. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector fields. First, we provide a canonical form for these systems assuming that each linear system has center, a real one for y0, and such that the real center is a global center. Then, working with a first order piecewise linear perturbation we obtain piecewise linear differential systems with three crossing limit cycles. Second, we see that a sliding cycle can be detected after a second order piecewise linear perturbation. Finally, imposing the existence of a sliding limit cycle we prove that only one adittional crossing limit cycle can appear. Furthermore, we also characterize the stability of the higher amplitude limit cycle and of the infinity. The main techniques used in our proofs are the Melnikov method, the Extended Chebyshev systems with positive accuracy, and the Bendixson transformation.
Related Links	http://arxiv.org/pdf/1905.06427
Ending Page	514
Page Count	25
Starting Page	490
ISSN	14689367
e-ISSN	14689375
DOI	10.1080/14689367.2020.1722064
Journal	Dynamical Systems
Issue Number	3
Volume Number	35
Language	English
Publisher	Informa UK Limited
Publisher Date	2020-02-10
Access Restriction	Open
Subject Keyword	Journal: Dynamical Systems Mathematics Mechanics Nonsmooth Differential System Filippov Systems Piecewise Linear Differential System Crossing Limit Cycles Sliding Limit Cycles 34c05 34c07 37g15
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science Applications

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