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Limit cycles for a class of discontinuous piecewise generalized Kukles differential systems

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Abstract

The present paper is devoted to study an estimative to the number of limit cycles which bifurcate from the periodic orbits of the linear center \(\dot{x}=y, \dot{y}=-x\) by the averaging method of first order when it is perturbed inside a class of discontinuous generalized Kukles differential systems defined in 2l-zones, \(l=1,2,3,\ldots \), in the plane.

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Acknowledgements

The first author is partially supported by FAPESP Grant 2012/18780-0 and the CNPq Grant 449655/2014-8. The second author is partially supported by FAPESP Grant “Projeto Temático” 2014/00304-2. The third author was supported by CNPq Fellowship Number 140292/2017-9. The authors are grateful to the referees for their valuable suggestions to improve this manuscript.

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Authors and Affiliations

  1. Departamento de Física, Quimica e Matemática, UFSCar, Sorocaba, SP, 18052-780, Brazil

    Ana C. Mereu

  2. Departamento de Matemática, ICMC-Universidade de São Paulo, Avenida Trabalhador São-carlense, 400, São Carlos, SP, 13566-970, Brazil

    Regilene Oliveira & Camila A. B. Rodrigues

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  1. Ana C. Mereu
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  2. Regilene Oliveira
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  3. Camila A. B. Rodrigues
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Correspondence to Ana C. Mereu.

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Mereu, A.C., Oliveira, R. & Rodrigues, C.A.B. Limit cycles for a class of discontinuous piecewise generalized Kukles differential systems. Nonlinear Dyn 93, 2201–2212 (2018). https://doi.org/10.1007/s11071-018-4319-6

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  • DOI: https://doi.org/10.1007/s11071-018-4319-6

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