Partial control of chaotic systems

Samuel Zambrano, Miguel A F Sanjuán, James A. Yorke

Research output: Contribution to journalArticlepeer-review


In a region in phase space where there is a chaotic saddle, all initial conditions will escape from it after a transient with the exception of a set of points of zero Lebesgue measure. The action of an external noise makes all trajectories escape faster. Attempting to avoid those escapes by applying a control smaller than noise seems to be an impossible task. Here we show, however, that this goal is indeed possible, based on a geometrical property found typically in this situation: the existence of a horseshoe. The horseshoe implies that there exist what we call safe sets, which assures that there is a general strategy that allows one to keep trajectories inside that region with control smaller than noise. We call this type of control partial control of chaos.

Original languageEnglish
Article number055201
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number5
Publication statusPublished - May 6 2008

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics


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