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Limit cycles for m-piecewise discontinuous polynomial Liénard differential equations

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Abstract

We provide lower bounds for the maximum number of limit cycles for the m-piecewise discontinuous polynomial differential equations \({\dot{x} = y+{\rm sgn}(g_m(x, y))F(x)}\), \({\dot{y} = -x}\), where the zero set of the function sgn(g m (x, y)) with m = 2, 4, 6, . . . is the product of m/2 straight lines passing through the origin of coordinates dividing the plane into sectors of angle 2π/m, and sgn(z) denotes the sign function.

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Catalonia, Spain

    Jaume Llibre

  2. Departamento de Matemática, Universidade Estadual de Campinas, Caixa Postal 6065, 13083-970, Campinas, SP, Brazil

    Marco Antonio Teixeira

Authors
  1. Jaume Llibre
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  2. Marco Antonio Teixeira
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Correspondence to Marco Antonio Teixeira.

Additional information

The first author is partially supported by a MICINN/FEDER Grant MTM2008-03437, by a AGAUR Grant number 2009SGR-0410 and by ICREA Academia. The second author is partially supported by a FAPESP-BRAZIL Grant 2007/06896-5. All the authors are also supported by the joint project CAPES-MECD Grant PHB-2009-0025-PC.

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Llibre, J., Teixeira, M.A. Limit cycles for m-piecewise discontinuous polynomial Liénard differential equations. Z. Angew. Math. Phys. 66, 51–66 (2015). https://doi.org/10.1007/s00033-013-0393-2

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