## Principles and applications of chaotic systems (1995)

Venue: | Communications of the ACM |

Citations: | 7 - 1 self |

### BibTeX

@ARTICLE{Ditto95principlesand,

author = {William Ditto and Toshinori Munakata},

title = {Principles and applications of chaotic systems},

journal = {Communications of the ACM},

year = {1995},

volume = {38},

pages = {96--102}

}

### OpenURL

### Abstract

the behavioral elements of chaos introduces a wide array of commercial applications to enhance, manipulate, or better control many current technical functions. 96 November 1995/Vol. 38, No. 11 COMMUNICATIONS OF THE ACM There lies a behavior between rigid regularity and randomness based on pure chance. It’s called a chaotic system, or chaos for short [5]. Chaos is all around us. Our notions of physical motion or dynamic systems have encompassed the precise clock-like ticking of periodic systems and the vagaries of dice-throwing chance, but have often been overlooked as a way to account for the more commonly

### Citations

828 |
Deterministic non-periodic flow
- Lorenz
(Show Context)
Citation Context ... bodies can exhibit unstable and unpredictable behavior. Thus is chaos born (but not yet named!). Edward Lorenz. Irregularity in a toy model of the weather displays first chaotic or strange attractor =-=[9]-=-. Tien-Yien Li and James A. Yorke. In paper “Period Three Implies Chaos,” introduced the term “Chaos Theory.” Robert M. May. Application of the logistic equation to ecology, showing chaotic population... |

286 |
Synchronization in chaotic systems
- Pecora, Carroll
- 1990
(Show Context)
Citation Context ...s thus difficult to construct synchronized chaotic systems. Lou Pecora and Tom Carroll, at the Naval Research Lab, considered how two identical or almost identical chaotic systems can be synchronized =-=[12]-=-. They take a chaotic system and produce a subsystem of the original by duplicating a part of the original system. They then supply a signal from the original to the subsystem. The original is unaware... |

85 |
Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series
- SUGIHARA, MAY
- 1990
(Show Context)
Citation Context ...rithms are sometimes controversial, due to a susceptibility to measurement error, researchers using such techniques claim to have identified measles as a chaotic disease but chicken pox as nonchaotic =-=[18]-=-. Other prediction problems. Other application domains, many of which are speculative, include cardiology, ecology, financial markets, economy, fluid flow, weather, and climate (e.g., the El Nino osci... |

37 |
L.,“A First Course in Chaotic Dynamical Systems: Theory and Experiment
- Devaney
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Citation Context ...-ran1978 dom number generators are chaotic but also periodic with certain periods. Such generators viewed carefully yield the hid1980 den order characteristic of chaos. (For more on fundamentals, see =-=[1, 2, 14]-=-). While this random number generator 1990 is an artificial chaotic system, there are numerous chaotic systems in nature. While engineers typically shun chaos and 1990 irregularity, nature may indeed ... |

30 |
Chaos: Making a New Science (Viking
- Gleick
- 1987
(Show Context)
Citation Context ...ctions. 96 November 1995/Vol. 38, No. 11 COMMUNICATIONS OF THE ACM There lies a behavior between rigid regularity and randomness based on pure chance. It’s called a chaotic system, or chaos for short =-=[5]-=-. Chaos is all around us. Our notions of physical motion or dynamic systems have encompassed the precise clock-like ticking of periodic systems and the vagaries of dice-throwing chance, but have often... |

24 |
Coping with chaos – analysis of chaotic data and the exploitation of chaotic systems
- Ott, Sauer, et al.
- 1994
(Show Context)
Citation Context ...dustrial applications, based on different aspects of chaotic systems (see Tables 2 and 3). For simplicity, we classify the application types into the categories stabilization, synthesis, and analysis =-=[11]-=-. Stabilization and control. The extreme sensitivity of chaotic systems to tiny perturbations can be manipulated to stabilize or control the systems. The fundamental idea is that tiny perturbations ca... |

23 |
Communicating with chaos,” Phys
- Hayes, Grebogi, et al.
- 1993
(Show Context)
Citation Context ...or-foe type. Chaos in Communications Researchers at the Army research labs have exploited the control of chaos by using small perturbations to make chaotic circuits follow prescribed symbol sequences =-=[6]-=-. Hayes and collaborators state, “The natural complexity thus provides a vehicle for information transmission in the usual sense.” They exploit a nonlinear electrical oscillator producing largeamplitu... |

18 |
Applied chaos theory: a paradigm for complexity
- Çambel
- 1993
(Show Context)
Citation Context ...-ran1978 dom number generators are chaotic but also periodic with certain periods. Such generators viewed carefully yield the hid1980 den order characteristic of chaos. (For more on fundamentals, see =-=[1, 2, 14]-=-). While this random number generator 1990 is an artificial chaotic system, there are numerous chaotic systems in nature. While engineers typically shun chaos and 1990 irregularity, nature may indeed ... |

17 | The Genetic Algorithm Fractal - Juliany, Vose - 1994 |

17 |
Dynamical Control of a Chaotic Laser: Experimental Stabilization of a Globally Coupled System
- Roy, Jr, et al.
- 1992
(Show Context)
Citation Context ...hrough small feedback signals by exploiting the extreme sensitivity of the system. The chaos controller worked beautifully in controlling the chaotic intensity fluctuations in Roy’s solid-state laser =-=[15]-=-. Control-of-chaos techniques have since been successfully applied to nuclear magnetic resonance laser systems. Belousov-Zhabotinsky chemical reaction. Chaos control was accepted as a viable technique... |

14 |
E.: Using small perturbations to control chaos. Nature 363
- Shinbrot, Grebogi, et al.
- 1993
(Show Context)
Citation Context ...the spacecraft nearsthe comet they wanted to investigate. If the system had been nonchaotic, large perturbations, and consequently large expenditures of fuel would have made such a mission impossible =-=[3, 17]-=-. Multimode laser. The green problem consists of the desire to have a cheap, stable laser capable of generating stable green laser light. The problem is that stable green lasers, unlike stable infrare... |

10 |
Controlling cardiac chaos,” Science 257
- Garfinkel, Spano, et al.
- 1992
(Show Context)
Citation Context ...rrhythmias). The chaotic beating of the rabbit heart tissue was converted to periodic beating through electrical stimuli applied at irregAI emerging technologies ular timing dictated by chaos control =-=[4]-=-. This application of chaos control has been patented by the inventors and licensed by a major medical company. Human trials are currently being performed. Many efforts to control spatio-temporal comp... |

2 |
Trajectories and orbital maneuvers for the ISEE-3/ICE comet mission
- Farquhar, Muhonen, et al.
- 1985
(Show Context)
Citation Context ...the spacecraft nearsthe comet they wanted to investigate. If the system had been nonchaotic, large perturbations, and consequently large expenditures of fuel would have made such a mission impossible =-=[3, 17]-=-. Multimode laser. The green problem consists of the desire to have a cheap, stable laser capable of generating stable green laser light. The problem is that stable green lasers, unlike stable infrare... |

1 | Keeping chaos at bay. Chaotic dynamics and control in electronic circuits (Advanced Technology/Tutorial - Hunt, Johnson - 1993 |

1 |
Circuits that get chaos in sync
- Neff, Carroll
- 1993
(Show Context)
Citation Context ... can strip away the chaos and recover the information. Hopefully, anyone intercepting the signals will see only a noisy, chaotic signal. This type of communication setup was built by Neff and Carroll =-=[10]-=-. Although secure communications using synchronized chaos would probably have to be more sophisticated than simply adding your signal to chaos to hide it, these accomplishments represent the first ste... |

1 |
Controlling chaos in the Belousov-Zhabotinsky reaction. Nature 361
- Masere, Showalter
- 1993
(Show Context)
Citation Context ...to apply chaos control. While the timid were doubting, Kenneth Showalter and associates promptly exhibited beautiful control in a chaotic chemical reaction: the Belousov-Zhabotinsky chemical reaction =-=[13]-=-. Under continuous flow of chemicals into the tank, the concentrations of the chemicals exhibit steady-state, periodic, and chaotic behavior. Small perturbations (applied according to chaos control th... |

1 |
About the Authors: WILLIAM DITTO is an assistant professor of physics at Georgia Tech where he and his colleagues have pioneered methods for controlling chaotic behavior. Current research interests include exploitation in control of chaos in physical and
- Wasserman
- 1993
(Show Context)
Citation Context ...onization of modules with chaotic behaviors that communicate through broad spectrum chaotic signals. We can construct or train a neural network so that its output exhibits a dynamic behavior of chaos =-=[19]-=-. COMMUNICATIONS OF THE ACM November 1995/Vol. 38, No. 11 101sFrom an engineering point of view, such a chaotic neural network may be applied for prediction and control. From a scientific point of vie... |