Stochastic synchronization of coupled coherence resonance oscillators

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 10, Issue 11, 2000, Pages 2541-2550

  Postnov, D E ^a   Sosnovtseva, O V ^a   Han, S K ^b   Yim, T G ^b  

^a SARATOV STATE UNIVERSITY   (Russian Federation)

^b Chungbuk National University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034310159     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127400001705     Document Type: Article

References (36)

1. Anishchenko, V. S., Vadivasova, T. E., Postnov, D. E. & Safonova, M. A. [1992] "Synchronization of chaos," Int. J. Bifurcation and Chaos 2, 633-644.
2. Anishchenko, V. S. [1995] Dynamical Chaos -Models and Experiments: Appearance Routes and Structure of Chaos in Simple Dynamical Systems (World Scientific, Singapore).
3. Anishchenko, V. S., Vadivasova, T. E., Postnov, D. E., Sosnovtseva, O. V., Wu, C. W. & Chua, L. O. [1995] "Dynamics of nonautonomous Chua's circuit," Int. J. Bifurcation and Chaos 5, 1525-1540.
4. Anishchenko, V. S., Silchenko, A. N. & Khovanov, I. A. [1998] "Synchronization of switching processes in coupled Lorenz systems," Phys. Rev. E57, 316-322.
5. Aronson, D. G., Ermentrout, G. B. & Kopell, N. [1990] "Amplitude response of coupled oscillators," Physica D41, 403-449.
6. Fedchenia, I. I., Mannella, R., McClintock, P. V. E., Stein, N. D. & Stocks, N.G. [1992] "Influence of noise on periodic attractors in the Lorenz model: Zero-frequency spectral peaks and chaos," Phys. Rev. A46, 1769-1774.
7. Gang, H., Ditzinger, T., Ning, C. Z. & Haken, H. [1993] "Stochastic resonance without external periodic force," Phys. Rev. Lett. 71, 807-810.
8. Han, S. K., Yim, T. G., Postnov, D. E. & Sosnovtseva, O. V. [1999] "Interacting coherence resonance oscillators," Phys. Rev. Lett. 83, 1771-1774.
9. Hänggi, P. & Bartussek, R. [1996] Nonlinear Physics of Complex Systems, Lecture Notes in Physics (Springer, Berlin).
10. Hayashi, C. [1964] Nonlinear Oscillations in Physical Systems (McGraw-Hill, NY).
11. Hodgkin, A. L. & Huxley, A. F. [1952] "A quantitative description of membrane current and its application to conduction and excitation in nerve," J. Physiol. 117, 500-544.
12. Julicher, F., Ajdari, A. & Prost, J. [1997] "Modeling molecular motors," Rev. Mod. Phys. 69(4), 1269-1281.
13. Kuramoto, Y. [1984] Chemical Oscillations, Waves and Turbulence (Springer, Berlin).
14. Kurrer, C. & Schulten, K. [1995] "Noise-induced synchronous neuronal oscillations," Phys. Rev. E51, 6213-6218.
15. Lee, S.-G., Neiman, A. & Kim, S., [1998] "Coherence resonance in a Hodgkin-Huxley neuron," Phys. Rev. E57, 3292-3297.
16. Longtin, A. [1997] "Autonomous stochastic resonance in bursting neurons," Phys. Rev. E55, 868-876.
17. Mayer-Kress, G. & Haken, H. [1981] "The influence of noise on the logistic model," J. Stat. Phys. 26, 149-171.
18. Morris, C. & Lecar, H. [1981] "Voltage oscillations in the barnacle giant muscle fiber," Biophys. J. 35, 193-213.
19. Moss, F., Bulsara, A. & Shlesinger, M. (eds.) [1993] Proc. NATO Advanced Research Workshop on Stochastic Resonance in Physics and Biology, J. Stat. Phys. 70, p. 1.
20. Neiman, A. B. [1994] "Synchronization like phenomena in coupled stochastic bistable systems," Phys. Rev. E49, 3484-3487.
21. Neiman, A., Saparin, P. I. & Stone, L. [1997] "Coherence resonance at noisy precursors of bifurcations in nonlinear systems," Phys. Rev. E56, 270-273.
22. Neiman, A., Silchenko, A., Anishchenko, V. & Schimansky-Geier, L. [1998] "Stochastic resonance: noise-enhanced phase coherence," Phys. Rev. E58, 7118-7125.
23. Neiman, A., Schimansky-Geier, L., Moss, F., Shulgin, B. & Collins, J. J. [1999] "Synchronization of noisy systems by stochastic signals," Phys. Rev. E60, 284-292.
24. Peckham, B. B. [1990] "The necessity of the Hopf bifurcation for periodically forced oscillators," Nonlinearity 3, 261-280.
25. Pikovsky, A. S. & Kurths, J. [1997] "Coherence resonance in a noise driven excitable system," Phys. Rev. Lett. 78, 775-778.
26. Pikovsky, A. S., Rosenblum, M. G., Osipov, G. V. & Kurths, J. [1997] "Phase synchronization of chaotic oscillators by external driving," Physica D104, 219-238.
27. Postnov, D. E., Han, S. K., Yim, T. G. & Sosnovtseva, O. V. [1999] "Experimental observation of coherence resonance in cascaded excitable systems," Phys. Rev. E59, R3791-R3794.
28. Rajasekar, S. [1995] "Controlling of chaotic motion by chaos and noise signals in a logistic map and a Bonhoeffer-van der Pol oscillator," Phys. Rev. E51, 775-778.
29. Rappel, W.-J. & Strogatz, S. H. [1994] "Stochastic resonance in an autonomous system with a nonuniform limit cycle," Phys. Rev. E50, 3249-3250.
30. Rosenblum, M., Pikovsky, A. & Kurths, J. [1996] "Phase synchronization of chaotic oscillators," Phys. Rev. Lett. 76, 1804-1807.
31. Rosenblum, M. G., Kurths, J., Pikovsky, A., Schäfer, C., Tass, P. & Abel, H.-H. [1998] "Synchronization in noisy systems and cardiorespiratory interaction," IEEE Eng. Med. Biol. Mag. 17(6), 46-53.
32. Shulgin, B. V., Neiman, A. B. & Anishchenko, V. S. [1995] "Mean switching frequency locking in stochastic bistable systems driven by a periodic force," Phys. Rev. Lett. 75, 4157-4160.
33. Stratonovich, R. L. [1967] Topics in the Theory of the Random Noise (Gordon and Breach, NY).
34. Treutlein, H. & Schulten, K. [1985] "Noise-induced limit cycles of the Bonhoeffer-van der Pol model of neural pulses," Ber. Bunsen-Ges. Phys. Chem. 89, 710-718.
35. Treutlein, H. & Schulten, K. [1986] "Noise-induced neural impulses," Eur. Biophys. J. 13, 355-356.
36. Van der Pol, B. [1920] "Theory of the amplitude of free and forced triode vibration," Radio Rev. 1, 701-710.