Stabilization, by means of small system perturbations, of unstable periodic orbits
This article is about chaos observed within non-linear systems. For other uses, see Chaos Control (disambiguation).
In lab experiments that study chaos theory, approaches designed to control chaos are based on certain observed system behaviors. 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.[1]
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 compared to the overall size of the attractor of the system to avoid significant modification of the system's natural dynamics.[2]
Several techniques have been devised for chaos control, but most are developments of two basic approaches: the Ott–Grebogi–Yorke (OGY) 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.
^González-Miranda, J.M. (2004). Synchronization and Control of Chaos: An Introduction for Scientists and Engineers. London: Imperial College Press. Bibcode:2004scci.book.....G.
^Eckehard Schöll and Heinz Georg Schuster (2007). Handbook of Chaos Control. Weinheim: Wiley-VCH.
ChaosControl may refer to: ChaosControl (video game), a 1995 video game The ability possessed by certain characters in Sonic the Hedgehog Control of...
In lab experiments that study chaos theory, approaches designed to controlchaos are based on certain observed system behaviors. Any chaotic attractor...
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical...
Synchronization ofchaos is a phenomenon that may occur when two or more dissipative chaotic systems are coupled. Because of the exponential divergence of the nearby...
clear that such types ofcontrol goals are important not only for the controlofchaos, but also for the controlof a broader class of oscillatory processes...
ChaosChaos are an American indie synthpop band based in Brooklyn, New York. The band was formed in Seattle under the name Smoosh in 2000 and adopted...
Lord ofChaos is a fantasy novel by American author Robert Jordan, the sixth book of his series The Wheel of Time. It was published by Tor Books and released...
Evolution ofChaos is the third studio album by American thrash metal band Heathen. It is their first album in 18 years since 1991's Victims of Deception...
A Great Chaos is the third studio album by American rapper Ken Carson. It was released through Opium and Interscope Records on October 13, 2023. The album...
to one of two chaotic phenomena: synchronization ofchaos, or controlofchaos. To implement chaos communications using such properties ofchaos, two chaotic...
Chaos magic, also spelled chaos magick, is a modern tradition of magic. Emerging in England in the 1970s as part of the wider neo-pagan and esotericist...
internalization of norms and values through socialization. Formal means comprise external sanctions enforced by government to prevent the establishment ofchaos or...
"Jean Dawson Controls the Chaos". W. Retrieved October 7, 2022. Barlas, Jon (October 7, 2022). "Jean Dawson balances chaos and control on Chaos Now*". Our...
The story ofChaos Legion is a gothic opera which begins November, 791 A.S. (Anno Satanis): the protagonist, Sieg Wahrheit, is a Knight of the Dark Glyphs...
Sonic Chaos is a 1993 platform game published by Sega for the Master System and Game Gear. Players control Sonic the Hedgehog and his sidekick Miles "Tails"...
Quantum chaos is a branch of physics which studies how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question...
The edge ofchaos is a transition space between order and disorder that is hypothesized to exist within a wide variety of systems. This transition zone...
controls the second player, so that one never has to fight the chaos alone. Controlof characters cannot be swapped once chosen. It is possible to play...
five-in-a-row of either Xs or Os. The opponent Chaos endeavors to prevent this. Unlike typical board games, both players control both sets of pieces (Xs...
Chaos Corona is a computer-generated imagery 3D rendering software developed by Chaos Czech, a subsidiary ofChaos. It was created by Ondřej Karlík as...
Global Information