Chaos: control and communication

Celso Grebogi, Ying Cheng Lai, Scott T. Hayes

Research output: Chapter in Book/Report/Conference proceedingConference contribution


This paper addresses two related issues: (1) control of chaos and, (2) controlling symbolic dynamics for communication. For control of chaos, we discuss the idea for realizing desirable periodic motion by applying small perturbations to an accessible parameter of the system. The key observations is that a chaotic attractor typically has embedded densely within it an infinite number of unstable periodic orbits. Since we wish to make only small controlling perturbations to the system, we do not envision creating new orbits with very different properties from the already existing orbits. Thus we seek to exploit the already existing unstable periodic orbits and unstable steady states. Our approach is as follows: We first determine some of the unstable low-period periodic orbits and unstable steady states that are embedded in the chaotic attractor. We then examine these orbits and choose one which yields improved system performance. Finally, we apply small controls so as to stabilize this already existing orbit. For the issue of communication, we describe an experiment verifying that the injection of small current pulses can be used to control the symbolic dynamics of a chaotic electrical oscillator to produce a digital communication waveform.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
EditorsNeal B. Abraham, Yakov I. Khanin
Number of pages15
StatePublished - Jan 1 1996
Externally publishedYes
EventLaser Optics '95: Nonlinear Dynamics in Lasers - St. Petersburg, Russia
Duration: Jun 27 1995Jul 1 1995

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X


OtherLaser Optics '95: Nonlinear Dynamics in Lasers
CitySt. Petersburg, Russia

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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