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Stochastic resonance in chaotically forced systems. (English) Zbl 0778.58039

Summary: The realization of stochastic resonance in chaotically forced systems is discussed and a new measure of it is introduced.

MSC:

37A99 Ergodic theory
Full Text: DOI

References:

[1] Benzi, R.; Sutera, A.; Vulpiani, A., The mechanism of stochastic resonance, J. Phys. A: Math. Gen., 14, L453-L457 (1981)
[2] Benzi, R.; Parisi, G.; Sutera, A.; Vulpiani, A., Stochastic resonance in climatic change, Tellus, 34, 10-16 (1982)
[3] Benzi, R.; Parisi, G.; Sutera, A.; Vulpiani, A., A theory of stochastic resonance in climatic change, SIAM J. Appl. Math., 43, 565-578 (1983) · Zbl 0509.60059
[4] McNamara, B.; Wisenfeld, K.; Roy, R., Observation of stochastic resonance in a ring laser, Phys. Rev. Lett., 60, 2626-2629 (1988)
[5] Gammaitoni, L.; Marchesoni, F.; Menichella-Saetta, E.; Santucci, S., Stochastic resonance in bistable systems, Phys. Rev. Lett., 62, 349-352 (1989) · Zbl 0872.70015
[6] Fox, R. F., Stochastic resonance in a double well, Phys. Rev., 39A, 4148-4153 (1989)
[7] McNamara, B.; Wiesenfeld, K., Theory of stochastic resonance, Phys. Rev., 39A, 4854-4869 (1989)
[8] Vemuri, G.; Roy, R., Stochastic resonance in a bistable ring laser, Phys. Rev., 39A, 4668-4674 (1989)
[9] Gammaitoni, L.; Menichella-Saetta, E.; Santucci, S.; Marchesoni, F.; Presilla, C., Periodically time-modulated bistable systems: stochastic resonance, Phys. Rev., 40A, 2114-2119 (1989)
[10] Zhou, T.; Moss, F.; Jung, P., Escape-time distributions of a periodically modulated bistable system with noise, Phys. Rev., 42A, 3161-3169 (1990)
[11] Moss, F., Stochastic resonance, Ber. Bunsenges. Phys. Chem., 95, 303-311 (1991)
[12] Fraser, S.; Kapral, R., Periodic dichotomous-noise-induced transitions and stochastic resonance, Phys. Rev., 45A, 4100-4113 (1992)
[13] Anishchenko, V. S.; Safonova, M. A.; Chua, L. O., Stochastic resonance in Chua’s circuit, Int. J. Bifurcation Chaos, 2, 397-401 (1992) · Zbl 0875.94132
[14] Pecora, L.; Carroll, T. S., Synchronization in chaotic systems, Phys. Rev. Lett., 64, 821-824 (1990) · Zbl 0938.37019
[15] Pecora, L.; Carroll, T. S., Pseudoperiodic driving: eliminating multiple domains of attraction using chaos, Phys. Rev. Lett., 67, 945-948 (1991) · Zbl 0990.37504
[16] Pecora, L.; Carroll, T. S., Synchronizing chaotic circuits, IEEE Trans. Circuits Systems, 38, 453-456 (1991)
[17] Endo, T.; Chua, L. O., Synchronizing chaos from electronic phase-locked loops, Int. J. Bifurcation Chaos, 1, 701-710 (1991) · Zbl 0875.93175
[18] Ott, E.; Grebogi, C.; Yorke, J. A., Controlling chaos, Phys. Rev. Lett., 64, 1196-1199 (1990) · Zbl 0964.37501
[19] Afraimovich, V. S.; Verichev, N. N.; Rabinovich, M. I., Stochastic synchronization of oscillations in dissipative systems, Radiophys. Quantum Electron., 29, 795-803 (1986)
[20] Yamada, T.; Fukushima, K.; Yazaki, T., A new type of intermittency in an electronic circuit, Prog. Theor. Phys., 99, 120-130 (1989)
[21] Pikovsky, A. S.; Grassberger, P., Symmetry breaking bifurcation for coupled chaotic attractors, J. Phys. A: Math. Gen., 24, 4587-4597 (1991) · Zbl 0766.58031
[22] Anishchenko, V. S.; Vadivasova, T. E.; Postnov, D. E.; Safonova, M. A., Forced and mutual synchronization of chaos, Radio Engng Electron., 36, 338-351 (1991)
[23] Gullicksen, J.; Lieberman, A.; Sherman, R.; Lichtenberg, A. J.; Huang, I. Y.; Wonchoba, W.; Stenberg, M.; Khoury, P., Secure communication by synchronization to a chaotic signal, (Vohra, S.; Spano, M.; Shlesinger, M.; Pecora, L.; Ditto, W., Proceedings of the 1st Experimental Chaos Conference (1992), World Scientific: World Scientific Singapore)
[24] Kocarev, Lj.; Halle, K. S.; Eckert, K.; Chua, L. O.; Parlitz, U., Experimental demonstration of secure communications via chaotic synchronization, Int. J. Bifurcation Chaos, 2, 709-713 (1992) · Zbl 0875.94134
[25] Guckenheimer, J.; Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (1983), Springer: Springer New York · Zbl 0515.34001
[26] Anischenko, V. S., Interaction of attractors: intermittency of the chaos-chaos type, Lett. J. Tech. Phys., 10, 629-633 (1984)
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