Ott, Edward Department of Electrical Engineering, Institute for Plasma Research, University of Maryland, College Park, Maryland.
- Exponential sensitivity
- Unstable periodic orbits
- Controlling chaos
- Example of chaos control
- Links to Primary Literature
- Additional Readings
The branch of science known as chaotic dynamics originated with work done around 1900 by the mathematician H. Poincaré. His work and that of others have led to a basic understanding that even very simple systems can evolve with time in a very complex manner. In viewing such time evolution, words such as wild, random, and turbulent come to mind. Furthermore, this basic type of motion is extremely common and occurs in a vast variety of fields. Examples are the motion of thermally convecting fluids, the fluctuations of light intensity in certain laser systems, the motion of celestial bodies (for example, two planets circling a star), and even the irregular beating of a diseased heart. Recently, researchers have realized that chaotic motions can be controlled by means of small perturbing forces. That is, the natural, free-running chaotic motion can be altered in a predetermined way so as to improve the performance of an otherwise chaotic system. This article describes the principles of chaos control and some recent developments in this area. The key defining attribute of chaos that allows the achievement of control with only small perturbations is exponential sensitivity.
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