Adaptive strategies for recognition, control and synchronization of chaos

Chaos, Solitons and Fractals

Volumn 8, Issue 9, 1997, Pages 1431-1448

  Boccaletti, S ^a   Farini, A ^a   Arecchi, F T ^a,b  

^a ISTITUTO NAZIONALE DI OTTICA   (Italy)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE ALGORITHMS; CONTROL THEORY; SYNCHRONIZATION;

CHAOS CONTROL; CHAOS RECOGNITION; CHAOS SYNCHRONIZATION; CHAOTIC LORENTZ SYSTEM; MACKEY GLASS SYSTEMS; ROSSLER SYSTEMS;

CHAOS THEORY;

EID: 0031236791     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(96)00169-5     Document Type: Article

References (47)

1. Arecchi, F. T., Basti, G., Boccaletti, S. and Perrone, A. L., Adaptive recognition of a chaotic dynamics. Europhys. Lett., 1994, 26, 327; Arecchi, F. T., Basti, G., Boccaletti, S. and Perrone, A. L., Adaptive recognition of chaos. Int. J. Bifurcation and Chaos, 1994, 4, 1275.
2. Arecchi, F. T., Basti, G., Boccaletti, S. and Perrone, A. L., Adaptive recognition of a chaotic dynamics. Europhys. Lett., 1994, 26, 327; Arecchi, F. T., Basti, G., Boccaletti, S. and Perrone, A. L., Adaptive recognition of chaos. Int. J. Bifurcation and Chaos, 1994, 4, 1275.
3. Boccaletti, S. and Arecchi, F. T., Adaptive control of chaos. Europhys. Lett., 1995, 31, 127; Boccaletti, S. and Arecchi, F. T., Adaptive recognition and control of chaos. Physica, 1996, D96, 9.
4. Boccaletti, S. and Arecchi, F. T., Adaptive control of chaos. Europhys. Lett., 1995, 31, 127; Boccaletti, S. and Arecchi, F. T., Adaptive recognition and control of chaos. Physica, 1996, D96, 9.
5. Boccaletti, S., Farini, A. and Arecchi, F. T., Adaptive synchronization of chaos for secure communication. Submitted to Phys. Rev. Lett.
6. Grossberg, S., Nonlinear neural networks: principles. Mech. Architect. Neural Nets, 1988, 1, 17.
7. Basti, G. and Perrone, A. L., A theorem of computational effectiveness for a mutual redefinition of numbers and processes. Proc. Int. Symp. of Information Physics (ISKIT '92), Kyushu Institute of Technology, 1992, p. 122.
8. Lorenz, E. N., Deterministic nonperiodic flow. J. Atmos. Sci., 1963, 20, 130.
9. Rössler, O. E., An equation for continuous chaos. Phys. Lett., 1976, 57A, 397.
10. Rössler, O. E., An equation for hyperchaos. Phys. Lett., 1979, 71A, 155.
11. Mackey, M. C. and Glass, L., Oscillation and chaos in physiological control systems. Science, 1977, 197, 287.
12. Farmer, J. D., Chaotic attractors of an infinite-dimensional dynamical system. Physica, 1982, D4, 366; Grassberger, P. and Procaccia, I., Measuring the strangeness of strange attractors. Physica, 1983, D9, 189.
13. Farmer, J. D., Chaotic attractors of an infinite-dimensional dynamical system. Physica, 1982, D4, 366; Grassberger, P. and Procaccia, I., Measuring the strangeness of strange attractors. Physica, 1983, D9, 189.
14. Theiler, J., Galdrikian, J., Longtin, A., Eubank, S. and Farmer, J. D., In Nonlinear Modeling and Forecasting, eds M. Casdagli and S. Eubank. Addison-Wesley, Reading, MA, 1992.
15. Grassberger, P. and Procaccia, I., Characterization of strange attractors. Phys. Rev. Lett., 1983, 50, 346.
16. Badii, R. and Politi, A., Hausdorff dimension and uniformity factor of strange attractors. Phys. Rev. Lett., 1984, 52, 1661.
17. Kaplan, D. T. and Glass, L., Direct test for determinism in a time series. Phys. Rev. Lett., 1992, 68, 427; Wayland, R., Bromley, D., Pickett, D. and Passamante, A., Recognizing determinism in a time series. Phys. Rev. Lett., 1993, 70, 580.
18. Kaplan, D. T. and Glass, L., Direct test for determinism in a time series. Phys. Rev. Lett., 1992, 68, 427; Wayland, R., Bromley, D., Pickett, D. and Passamante, A., Recognizing determinism in a time series. Phys. Rev. Lett., 1993, 70, 580.
19. Auerbach, D., Cvitanovic, P., Eckmann, J.-P., Gunaratne, G. and Procaccia, I., Exploring chaotic motion through periodic orbits. Phys. Rev. Lett., 1987, 58, 2387.
20. Ott, E., Grebogi, C. and Yorke, J. A., Controlling chaos. Phys. Rev. Lett., 1990, 64, 1196.
21. Shinbrot, T., Grebogi, C., Ott, E. and Yorke, J. A. Using small perturbations to control chaos. Nature, 1993, 363, 411.
22. Plapp, B. B. and Huebler, A. W., Nonlinear resonances and suppression of chaos in the rf-biased Josephson junction. Phys. Rev. Lett., 1990, 65, 2302; Jackson, E. A. and Huebler, A. W., Periodic entrainment of chaotic logistic map dynamics. Physica, 1990, D44, 407; Jackson, E. A., Controls of dynamic flows with attractors. Phys. Rev., 1991, A44, 4839.
23. Plapp, B. B. and Huebler, A. W., Nonlinear resonances and suppression of chaos in the rf-biased Josephson junction. Phys. Rev. Lett., 1990, 65, 2302; Jackson, E. A. and Huebler, A. W., Periodic entrainment of chaotic logistic map dynamics. Physica, 1990, D44, 407; Jackson, E. A., Controls of dynamic flows with attractors. Phys. Rev., 1991, A44, 4839.
24. Plapp, B. B. and Huebler, A. W., Nonlinear resonances and suppression of chaos in the rf-biased Josephson junction. Phys. Rev. Lett., 1990, 65, 2302; Jackson, E. A. and Huebler, A. W., Periodic entrainment of chaotic logistic map dynamics. Physica, 1990, D44, 407; Jackson, E. A., Controls of dynamic flows with attractors. Phys. Rev., 1991, A44, 4839.
25. Lima, R. and Pettini, M., Suppression of chaos by resonant parametric perturbations. Phys. Rev., 1990, A41, 726; Braiman, Y. and Goldhirsch, I., Taming chaotic dynamics with weak periodic perturbations. Phys. Rev. Lett., 1991, 66, 2545.
26. Lima, R. and Pettini, M., Suppression of chaos by resonant parametric perturbations. Phys. Rev., 1990, A41, 726; Braiman, Y. and Goldhirsch, I., Taming chaotic dynamics with weak periodic perturbations. Phys. Rev. Lett., 1991, 66, 2545.
27. Azevedo, A. and Rezende, S. M., Controlling chaos in spin-wave instabilities. Phys. Rev. Lett., 1991, 66, 1342.
28. Fahy, S. and Hamann, D. R., Transition from chaotic to nonchaotic behavior in randomly driven systems. Phys. Rev. Lett., 1992, 69, 761.
29. Pyragas, K., Continuous control of chaos by self-controlling feedback. Phys. Lett., 1992, A170, 421.
30. Singer, J., Wang, Y.-Z. and Bau, H. H., Controlling a chaotic system. Phys. Rev. Lett., 1991, 66, 1123.
31. Hunt, E. R., Stabilizing high-period orbits in a chaotic system: the diode resonator. Phys. Rev. Lett., 1991, 67, 1953.
32. Roy, R., Murphy, T. W. Jr, 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., 1992, 68, 1259.
33. Peng, B., Petrov, V. and Showalter, K., Controlling chemical chaos. J. Phys. Chem., 1991, 95, 4957; Petrov, V., Gaspar, V., Masere, J. and Showalter, K., Controlling chaos in the Belousov-Zhabotinsky reaction, Nature, 1993, 361, 240.
34. Peng, B., Petrov, V. and Showalter, K., Controlling chemical chaos. J. Phys. Chem., 1991, 95, 4957; Petrov, V., Gaspar, V., Masere, J. and Showalter, K., Controlling chaos in the Belousov-Zhabotinsky reaction, Nature, 1993, 361, 240.
35. Meucci, R., Gadomski, W., Ciofini, M. and Arecchi, F. T., Experimental control of chaos by means of weak parametric perturbations. Phys. Rev., 1994, E49, R2528.
36. Romeiras, F. J., Grebogi, C., Ott, E. and Dayawansa, W. P., Controlling chaotic dynamical systems. Physica, 1992, D58, 165.
37. Kostelich, E. J., Grebogi, C., Ott, E. and Yorke, J. A., Higher-dimensional targeting. Phys. Rev., 1993, E47, 305.
38. Cvitanovic, P., Gunaratne, G. H. and Procaccia, I., Topological and metric properties of Hénon-type strange attractors. Phys. Rev., 1988, A38, 1503; Gunaratne, G. H., Linsay, P. S. and Vinson, M. J., Chaos beyond onset: a comparison of theory and experiment. Phys. Rev. Lett., 1989, 63, 1; Mindlin, G. B., Hou, X.-J., Solari, H. G., Gilmore, R. and Tufillaro, N. B., Classification of strange attractors by integers. Phys. Rev. Lett., 1990, 64, 2350; Tufillaro, N. B., Solari, H. G. and Gilmore, R., Relative rotation rates: fingerprints for strange attractors. Phys. Rev., 1990, A41, R5717.
39. Cvitanovic, P., Gunaratne, G. H. and Procaccia, I., Topological and metric properties of Hénon-type strange attractors. Phys. Rev., 1988, A38, 1503; Gunaratne, G. H., Linsay, P. S. and Vinson, M. J., Chaos beyond onset: a comparison of theory and experiment. Phys. Rev. Lett., 1989, 63, 1; Mindlin, G. B., Hou, X.-J., Solari, H. G., Gilmore, R. and Tufillaro, N. B., Classification of strange attractors by integers. Phys. Rev. Lett., 1990, 64, 2350; Tufillaro, N. B., Solari, H. G. and Gilmore, R., Relative rotation rates: fingerprints for strange attractors. Phys. Rev., 1990, A41, R5717.
40. Cvitanovic, P., Gunaratne, G. H. and Procaccia, I., Topological and metric properties of Hénon-type strange attractors. Phys. Rev., 1988, A38, 1503; Gunaratne, G. H., Linsay, P. S. and Vinson, M. J., Chaos beyond onset: a comparison of theory and experiment. Phys. Rev. Lett., 1989, 63, 1; Mindlin, G. B., Hou, X.-J., Solari, H. G., Gilmore, R. and Tufillaro, N. B., Classification of strange attractors by integers. Phys. Rev. Lett., 1990, 64, 2350; Tufillaro, N. B., Solari, H. G. and Gilmore, R., Relative rotation rates: fingerprints for strange attractors. Phys. Rev., 1990, A41, R5717.
41. Cvitanovic, P., Gunaratne, G. H. and Procaccia, I., Topological and metric properties of Hénon-type strange attractors. Phys. Rev., 1988, A38, 1503; Gunaratne, G. H., Linsay, P. S. and Vinson, M. J., Chaos beyond onset: a comparison of theory and experiment. Phys. Rev. Lett., 1989, 63, 1; Mindlin, G. B., Hou, X.-J., Solari, H. G., Gilmore, R. and Tufillaro, N. B., Classification of strange attractors by integers. Phys. Rev. Lett., 1990, 64, 2350; Tufillaro, N. B., Solari, H. G. and Gilmore, R., Relative rotation rates: fingerprints for strange attractors. Phys. Rev., 1990, A41, R5717.
42. Pecora, L. M. and Carrols, T. L., Synchronization in chaotic systems. Phys. Rev. Lett., 1990, 64, 821.
43. Hayes, S., Grebogi, C., Ott, E. and Mark, A., Experimental control of chaos for communication. Phys. Rev. Lett., 1994, 73, 1781.
44. Cuomo, K. M. and Oppenheim, A. V., Circuit implementation of synchronized chaos with application to communications. Phys. Rev. Lett., 1993, 71, 65.
45. Perez, G. and Cerdeira, H. A., Extracting messages masked by chaos. Phys. Rev. Lett., 1995, 74, 1970.
46. Peng, J. H., Ding, E. J., Ding, M. and Yang, W., Synchronizing hyperchaos with a scalar transmitted signal. Phys. Rev. Lett., 1996, 76, 904.
47. Ding, M. and Ott, E., Enhancing synchronism of chaotic system. Phys. Rev., 1994, E49, R945.