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Occurrence of multiple attractor bifurcations in the two-dimensional piecewise linear normal form map

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Abstract

Multiple attractor bifurcations occurring in piecewise smooth dynamical systems may lead to potentially damaging situations. In order to avoid these in physical systems, it is necessary to know their conditions of occurrence. Using the piecewise-linear 2D normal form, we investigate which types of multiple attractor bifurcations may occur and where in the parameter space they can be expected. For piecewise smooth maps, multiple attractor bifurcations will be expected to occur if the condition we identified for the piecewise-linear 2D normal form are satisfied in the close neighborhood of the border.

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Authors and Affiliations

  1. University of Stuttgart, Stuttgart, Germany

    Viktor Avrutin & Michael Schanz

  2. Indian Institute of Science Education and Research–Kolkata, Mohanpur Campus, Nadia, 741252, West Bengal, India

    Soumitro Banerjee

Authors
  1. Viktor Avrutin
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  2. Michael Schanz
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  3. Soumitro Banerjee
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Correspondence to Viktor Avrutin.

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Avrutin, V., Schanz, M. & Banerjee, S. Occurrence of multiple attractor bifurcations in the two-dimensional piecewise linear normal form map. Nonlinear Dyn 67, 293–307 (2012). https://doi.org/10.1007/s11071-011-9978-5

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