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On Double Boundary Equilibrium Bifurcations in Piecewise Smooth Planar Systems

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Abstract

In this paper we contribute to the study of codimension-two bifurcations in piecewise smooth (PWS) planar dynamical systems by considering boundary equilibria bifurcations, that is, collisions of an equilibrium point with the discontinuity boundary. First, an improved proof of the characterization theorem for boundary equilibria bifurcations in this class of systems is given. Next, we analyze an specific family in 2D Filippov systems where the simultaneous appearance of two boundary equilibrium bifurcations is possible. The bifurcation set obtained illustrates the complexity of dynamical behavior that can be found in simple non-smooth piecewise linear systems. The case studied seems to be a section of a higher codimension bifurcation point, since it shows the nearby existence of three codimension two points: the double boundary equilibrium point and two homoclinic boundary focus bifurcation points.

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Authors and Affiliations

  1. Department of Automation and Systems, Universidade Federal de Santa Catarina, Florianópolis, Brazil

    Daniel J. Pagano

  2. Department of Applied Mathematics, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Camino de los Descubrimientos, 41092, Seville, Spain

    Enrique Ponce & Francisco Torres

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  1. Daniel J. Pagano
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  2. Enrique Ponce
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  3. Francisco Torres
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Correspondence to Enrique Ponce.

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Pagano, D.J., Ponce, E. & Torres, F. On Double Boundary Equilibrium Bifurcations in Piecewise Smooth Planar Systems. Qual. Theory Dyn. Syst. 10, 277–301 (2011). https://doi.org/10.1007/s12346-011-0050-0

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  • DOI: https://doi.org/10.1007/s12346-011-0050-0

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