Chaotic behavior of driven, second-order, piecewise linear systems

Jose Castro*, Joaquin Alvarez, Fernando Verduzco, Juan E. Palomares-Ruiz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


In this paper the chaotic behavior of second-order, discontinuous systems with a pseudo-equilibrium point on a discontinuity surface is analyzed. The discontinuous system is piecewise linear and approximated to a non-smooth continuous system. The discontinuous term is represented by a sign function that is replaced by a saturation function with high slope. Some of the conditions that determine the chaotic behavior of the approximate system are formally established. Besides, the convergence of its chaotic solutions to those of the discontinuous system is shown. Several bifurcation diagrams of both systems show the similarity of their dynamical behavior in a wide parameter range, and particularly for a parameter region determined from the application of the Melnikov technique to non-smooth systems, where a chaotic behavior can be displayed.

Original languageEnglish
Pages (from-to)8-13
Number of pages6
JournalChaos, Solitons and Fractals
StatePublished - Dec 2017

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Ltd


  • Approximation techniques
  • Continuous systems
  • Discontinuous systems
  • Melnikov function
  • Piecewise smooth system


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