Exploring partial control of chaotic systems

Samuel Zambrano, Miguel A F Sanjuán

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we make a thorough exploration of the technique of partial control of chaotic systems. This control technique allows one to keep the trajectories of a dynamical system close to a chaotic saddle even if the control applied is smaller than the effects of environmental noise in the system, provided that the chaotic saddle is due to the existence of a horseshoelike mapping in phase space. We state this here in a mathematically precise way using the Conley-Moser conditions, and we prove that they imply that our partial control strategy can be applied. We also give an upper bound of the control-noise ratio needed to achieve this goal, and we describe how this technique can be applied for large noise values. Finally, we study in detail the effect of imperfect targeting in our control technique. All these results are illustrated numerically with the paradigmatic Hénon map.

Original languageEnglish
Article number026217
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume79
Issue number2
DOIs
Publication statusPublished - Feb 2 2009

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

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