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.

Mathematics Subject Classification (1991)

34C29 34C25 47H11 

Keywords

Limit cycle Liénard equation Piecewise differential equation Averaging method 
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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterra, BarcelonaSpain
  2. 2.Departamento de MatemáticaUniversidade Estadual de CampinasCampinasBrazil

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