Local cyclicity in low degree planar piecewise polynomial vector fields

In this work, we are interested in isolated crossing periodic orbits in planar piecewise polynomial vector fields defined in two zones separated by a straight line. In particular, in the number of limit cycles of small amplitude. They are all nested and surrounding one equilibrium point or a sliding...

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Bibliographic Details
Published in:Nonlinear analysis: real world applications 2021-08, Vol.60, p.103278, Article 103278
Main Authors: Gouveia, Luiz F.S., Torregrosa, Joan
Format: Article
Language:English
Subjects:
Lyapunov quantities
Piecewise center cyclicity
Piecewise vector field
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Summary:In this work, we are interested in isolated crossing periodic orbits in planar piecewise polynomial vector fields defined in two zones separated by a straight line. In particular, in the number of limit cycles of small amplitude. They are all nested and surrounding one equilibrium point or a sliding segment. We provide lower bounds for the local cyclicity for planar piecewise polynomial systems, Mpc(n), with degrees 2, 3, 4, and 5. More concretely, Mpc(2)≥13,Mpc(3)≥26,Mpc(4)≥40, and Mpc(5)≥58. The computations use parallelization algorithms.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2020.103278