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Limit cycles in a family of discontinuous piecewise linear differential systems with two zones in the plane

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Abstract

In this paper we study the existence of limit cycles in a one-parameter family of discontinuous piecewise linear differential systems with two zones in the plane. It is characterized for all the parameter values the number of non-sliding limit cycles of the family studied, detecting a rather non-generic bifurcation leading to the simultaneous generation of three limit cycles.

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Acknowledgements

The second author is partially supported by CNPq grant 301758/2012-3 and by FAPEMIG grant PPM-00204-11.

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Authors and Affiliations

  1. Campus Avançado de Itabira, Universidade Federal de Itajubá, Rua São Paulo 377, Bairro Amazonas, CEP 35.900-373, Itabira, MG, Brazil

    Denis de Carvalho Braga

  2. Instituto de Matemática e Computação, Universidade Federal de Itajubá, Avenida BPS 1303, Pinheirinho, CEP 37.500-903, Itajubá, MG, Brazil

    Luis Fernando Mello

Authors
  1. Denis de Carvalho Braga
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  2. Luis Fernando Mello
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Correspondence to Luis Fernando Mello.

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de Carvalho Braga, D., Mello, L.F. Limit cycles in a family of discontinuous piecewise linear differential systems with two zones in the plane. Nonlinear Dyn 73, 1283–1288 (2013). https://doi.org/10.1007/s11071-013-0862-3

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  • DOI: https://doi.org/10.1007/s11071-013-0862-3

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