Partial control of transient chaos in electronic circuits

Alexandre Wagemakers, Samuel Zambrano, Miguel A F Sanjuán

Research output: Contribution to journalArticlepeer-review

Abstract

We present an analog circuit implementation of the novel partial control method, that is able to sustain chaotic transient dynamics. The electronic circuit simulates the dynamics of the one-dimensional slope-three tent map, for which the trajectories diverge to infinity for nearly all the initial conditions after behaving chaotically for a while. This is due to the existence of a nonattractive chaotic set: a chaotic saddle. The partial control allows one to keep the trajectories close to the chaotic saddle, even if the control applied is smaller than the effect of the applied noise, introduced into the system. Furthermore, we also show here that similar results can be implemented on a circuit that simulates a horseshoe-like map, which is a simple extension of the previous one. This encouraging result validates the theory and opens new perspectives for the application of this technique to systems with higher dimensions and continuous time dynamics.

Original languageEnglish
Article number1250032
JournalInternational Journal of Bifurcation and Chaos
Volume22
Issue number2
DOIs
Publication statusPublished - Feb 2012

Keywords

  • analog circuit
  • Partial control of chaos
  • transient chaos

ASJC Scopus subject areas

  • Applied Mathematics
  • General
  • Engineering(all)
  • Modelling and Simulation

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