Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-29T12:18:29.133Z Has data issue: false hasContentIssue false
  • English
  • Français

Maintaining Chaos

Published online by Cambridge University Press:  10 February 2011

Mark L. Spano ,
Visarath In  and
William L. Ditto
Mark L. Spano
Affiliation:
Naval Surface Warfare Center, White Oak Laboratory, Silver Spring, MD 20903
Visarath In
Affiliation:
Naval Surface Warfare Center, White Oak Laboratory, Silver Spring, MD 20903
William L. Ditto
Affiliation:
Georgia Institute of Technology, School of Physics, Atlanta, GA 30332
Get access

Abstract

The recognition of chaos as a new type of behavior for complex systems initially spurred efforts to avoid it and, later, to control it. Yet in many cases chaos may be beneficial. We present a method for maintaining chaos in physical systems and implement the method on a simple magnetomechanical system. Application to other systems is discussed briefly.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 459: Symposium Y – Materials for Smart Systems II , 1996 , 545
Copyright
Copyright © Materials Research Society 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1 Ott, E., Grebogi, C. and Yorké, J. A., Phys. Rev. Lett. 64, 1196 (1190).Google Scholar
2 Ditto, W. L., Rauseo, S. N. and Spano, M. L., Phys. Rev. Lett. 65, 3211 (1990).Google Scholar
3 Roy, R., Murphy, T. W., Maier, T. D., Gills, Z. and Hunt, E. R., Phys. Rev. Lett. 68, 1259 (1992).Google Scholar
4 Hunt, E. R., Phys. Rev. Lett. 67, 1953 (1991).Google Scholar
5 Petrov, V., Gaspar, V., Masere, J., and Showalter, K., Nature 361, 240 (1993).Google Scholar
6 Garfinkel, A., Spano, M. L., Ditto, W. L. and Weiss, J. N., Science 257, 1230 (1992).Google Scholar
7 Schiff, S. J.., Jerger, K., Duong, D. H., Chang, T., Spano, M. L., and Ditto, W. L., Nature 370, 615 (1994).Google Scholar
8 For a nice review, see Shinbrot, T. A., Grebogi, C., Ott, E., and Yorke, J. A., Nature 363, 411 (1993). Also of interest isGoogle Scholar
Ditto, W. L. and Pecora, L. M., Scientific American 269, 78 (1993).Google Scholar
9 For instance, some studies of heart rate variability suggest that losing complexity in the heart rate will increase the mortality rate of cardiac patients. See, for example, Woo, M. A., Stevenson, W. G., Moser, D. K., Harper, R. M. and Trelease, R., Am. Heart Jour. 123, 704 (1992);Google Scholar
Goldberger, A. L., Ann. Biomed. Engin. 18, 195 (1990); andGoogle Scholar
Goldberger, A. L., Rigney, D. R. and West, B. J., Scientific American 262, 42 (1990).Google Scholar
10 Ottino, J. M., Scientific American 260, 40 (1989);Google Scholar
Ottino, J. M., Muzzio, F. J., Tjahjadi, M., Franjione, J. G., Jana, S. C. and Kusch, H. A., Science 257, 754 (1992);Google Scholar
Ottino, J. M., Metcalfe, Guy and Jana, S. C., Proc. of the 2nd Exptl. Chaos Conf., p. 3–20, (World Scientific, Singapore, 1995).Google Scholar
11 Hively, Lee, Oak Ridge National Laboratory, private communication.Google Scholar
12 Yang, W., Ding, M., Mandeli, A. and Ott, E., Phys. Rev. E. 51, 102 (1995).Google Scholar
13 The statistics associated with the dwell times the system spends in the periodic motion are consistent with a type III intermittency. For in depth discussion of intermittency types see Berge, P., Pomeau, Y. and Vidal, C., Order Within Chaos (John Wiley & Sons and Hermann, Paris, 1984).Google Scholar
14 Ditto, W. L., Rauseo, S., Cawley, R., Grebogi, C., Hsu, G. H., Kostelich, E., Ott, E., Savage, H. T., Segnan, R., Spano, M. L. and Yorke, J. A., Phys. Rev. Lett. 63, 923 (1989).Google Scholar