- Control of chaos
In chaos theory, control of chaos is based on the fact that any chaotic attractor contains an infinite number of unstable periodic orbits. Chaotic dynamics then consists of a motion where the system state moves in the neighborhood of one of these orbits for a while, then falls close to a different unstable periodic orbit where it remains for a limited time, and so forth. This results in a complicated and unpredictable wandering over longer periods of time.
Control of chaos is the stabilization, by means of small system perturbations, of one of these unstable periodic orbits. The result is to render an otherwise chaotic motion more stable and predictable, which is often an advantage. The perturbation must be tiny, to avoid significant modification of the system's natural dynamics.
Several techniques have been devised for chaos control, but most are developments of two basic approaches: the OGY (Ott, Grebogi and Yorke) method, and Pyragas continuous control. Both methods require a previous determination of the unstable periodic orbits of the chaotic system before the controlling algorithm can be designed.
In the OGY method, small, wisely chosen, swift kicks are applied to the system once per cycle, to maintain it near the desired unstable periodic orbit. In the Pyragas method, an appropriate continuous controlling signal is injected into the system, whose intensity is practically zero as the system evolves close to the desired periodic orbit but increases when it drifts away from the desired orbit.
Experimental control of chaos by one or both of these methods has been achieved in a variety of systems, including turbulent fluids, oscillating chemical reactions, magneto-mechanical oscillators, and cardiac tissues. Sarnobat et al. (2000) attempt the control of chaotic bubbling with the OGY method and using electrostatic potential as the primary control variable.
The number of publications devoted to control of chaos is huge, see e.g. Chaos control bibliography (1997-2000)
Forcing two systems into the same state is not the only way to achieve synchronization of chaos. Both control of chaos and synchronization constitute parts of Cybernetical Physics. Cybernetical physics is a research area on the border between Physics and Control Theory.
- Sarnobat, S.U., “Modification, Identification & Control of Chaotic Bubbling via Electrostatic Potential”, Masters Thesis, University of Tennessee, Knoxville, August 2000. link
Eckehard Schöll and Heinz Georg Schuster (Eds). Handbook of Chaos Control Wiley-VCH; 2nd Revision, Enlarged edition (2007) Weinheim.
González-Miranda, J. M. (2004). Synchronization and Control of Chaos: An Introduction for Scientists and Engineers. London: Imperial College Press.
Fradkov A.L., Pogromsky A.Yu. (1998). Introduction to Control of Oscillations and Chaos. Singapore: World Scientific Publishers.
Wikimedia Foundation. 2010.
Look at other dictionaries:
Chaos communications — is an application of chaos theory which is aimed to provide security in the transmission of information performed through telecommunications technologies. By secure communications, one has to understand that the contents of the message… … Wikipedia
Chaos theory — This article is about chaos theory in Mathematics. For other uses of Chaos theory, see Chaos Theory (disambiguation). For other uses of Chaos, see Chaos (disambiguation). A plot of the Lorenz attractor for values r = 28, σ = 10, b = 8/3 … Wikipedia
Chaos Energy — Occult portal In various fantasy games and other fiction as well as in occultism, the term Chaos Energy describes some sort of magical energy. In some fictional universes, it can be found solidified in the form of stones. Examples include Chaos… … Wikipedia
Chaos theory in organizational development — refers to a subset of chaos theory which incorporates principles of quantum mechanics and presents them in a complex systems environment. Contents 1 Background 2 Elements of organization 2.1 Self organization … Wikipedia
Chaos Walking Trilogy — The Knife of Never Letting Go The Ask and the Answer Monsters of Men Author Patrick Ness Cover artist Lynne Condellon (design) John Picacio (painting) Country … Wikipedia
Chaos and Creation in the Backyard — Studio album by Paul McCartney Released … Wikipedia
Chaos and Creation in the Backyard — Студийный альбом Пола Маккартни Дата выпуска 12 сентября 2005 Записан зима 2003 весна 2005 Жанры рок Длительность 46:53 … Википедия
Chaos 2 — with a chain holding down its flipper so that it is safe between fights. Statistics Height 0.42 m (1.4 ft) Wi … Wikipedia
Chaos: The Battle of Wizards — Chaos cover art Developer(s) Julian Gollop Publisher(s) Games Workshop … Wikipedia
Chaos Overlords — Developer(s) Stick Man Games Publisher(s) New World Computing Designer(s) John K. Morris … Wikipedia