Nonlinear Dynamics

, Volume 93, Issue 4, pp 2201–2212 | Cite as

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

  • Ana C. MereuEmail author
  • Regilene Oliveira
  • Camila A. B. Rodrigues
Original Paper


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.


Piecewise polynomial differential systems Limit cycles Averaging theory Kukles systems 

Mathematics Subject Classification

37G15 34A36 



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. 1.Departamento de Física, Quimica e MatemáticaUFSCarSorocabaBrazil
  2. 2.Departamento de MatemáticaICMC-Universidade de São PauloSão CarlosBrazil

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