Abstract
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 observed chaotic behavior between these two extremes. When we see irregularity we cling to randomness and disorder for explanations. Why should this be so? Why is it that when the ubiquitous irregularity of engineering, physical, biological, and other systems are studied, it is assumed to be random and the whole vast machinery of probability and statistics is applied? Rather recently, however, we have begun to realize that the tools of chaos theory can be applied toward the understanding, manipulation, and control of a variety of systems, with many of the practical applications coming after 1990. To understand why this is true, one must start with a working knowledge of how chaotic systems behave—profoundly, but sometimes subtly different, from the behavior of random systems.
- 1 Cambel, A.B. Applied Chaos Theory: A Paradigm for Complex~ Academic Press, San Diego, Calif., 1993.Google Scholar
- 2 Devaney, R.L. A First Course in Chaotic Dynamical Systems Theory and Experiment. Addison-Wesley, Reading, Mass., 1992.Google Scholar
- 3 Farquhar, R., Muhonen, D., and Church, L.C. Trajectories and orbital maneuvers for the ISEE-3/ICE comet mission. J. Astronaut. Sci. 33, 3 (July-Sept., 1985), 235-254.Google Scholar
- 4 Garfinkel, A., Spano, M. L., Ditto, W. L., and Weiss, J. A. Controlling cardiac chaos. Science 257, (1992), 1230-1235.Google ScholarCross Ref
- 5 Gleick, J. Chaos: Making a New Science. Viking Penguin, New York, 1987. Google ScholarDigital Library
- 6 Hayes, S., Grebogi, C., and Ott, E. Communicating with chaos, Phys. Rev. Lett. 70 (1993), 3031-3034.Google ScholarCross Ref
- 7 Hunt, E., and Johnson, G. Keeping chaos at bay. Chaotic dynamics and control in electronic circuits (Advanced Technology/Tutorial). 1EEE Spectrum 30 (Nov. 1993), 32-36.Google Scholar
- 8 Juliany, J., and Vose, M.D. The genetic algorithm fractal. In The Fifth International Conference on Genetic Algorithms (Urbana- Champaign, 1993), p. 639. Google ScholarDigital Library
- 9 Lorenz, E.N. Deterministic non-periodic flow. J. Atmos. Sci. 20, (1963), 130-141.Google ScholarCross Ref
- 10 Neff, J., and Carroll, T. Circuits that get chaos in sync. Sci. Am. 269, (Aug., 1993), 120-122.Google ScholarCross Ref
- 11 Ott, E., Sauer, T., and Yorke, J.A. Coping with Chaos: Analysis of Chaotic Data and the Exploitation of Chaotic Systems. Wiley, New York 1994.Google Scholar
- 12 Pecora, L.M., and Carroll, T.L. Synchronization in chaotic systems. Phys. Rev. Lett. 64, (1990), 821-824.Google ScholarCross Ref
- 13 Petrov, V., Gaspar, V,. Masere,J., and Showalter, K. Controlling chaos in the Belousov-Zhabotinsky reaction. Nature 361, (1993), 240-243.Google ScholarCross Ref
- 14 Proceedings of the 1EEE, Special issue on chaotic systems 75, 8 (Aug. 1987).Google Scholar
- 15 Roy, R., Murphy, T. W., Maier, T. D., Gills, Z., and Hunt, E. R. Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system. Phys. Rev. Lett. 68 (1992), 1259-1262.Google ScholarCross Ref
- 16 Schiff, S. J., Jerger, K., Duong, D. H., Chang, T., Spano, M. L., and Ditto, W.L. Controlling chaos in the brain. Nature, 370 (Aug. 25, 1994), 615-620.Google ScholarCross Ref
- 17 Shinbrot, T., Grebogi, C., Ott, E., and Yorke,J. A. Using small perturbations to control chaos. Nature 363 (June 3, 1993), 411-417.Google ScholarCross Ref
- 18 Sugihara, G., and May, R. M. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344 (Apr. 1990), 734-740.Google ScholarCross Ref
- 19 Wasserman, P.D. Advanced Methods in Neural Computing. Van Nostrand Reinhold, New York, 1993. Google ScholarDigital Library
Index Terms
- Principles and applications of chaotic systems
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