Optimal synchronization of chaotic systems in noise

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 46, Issue 11, 1999, Pages 1320-1329

  Zhu, Zhiwen ^a   Leung, Henry ^b   Ding, Zhen ^b  

^a MCMASTER UNIVERSITY   (Canada)

^b UNIVERSITY OF CALGARY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; ELECTRIC NETWORK SYNTHESIS; LYAPUNOV METHODS; SPURIOUS SIGNAL NOISE; SYNCHRONIZATION;

CHAOTIC DRIVE SYSTEMS;

CHAOS THEORY;

EID: 0033224861     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.802822     Document Type: Article

References (28)

1. H. Fujisaka and T. Yamada, "Stability theory of synchronized motion in coupled-oscillator systems," Prog. Theor. Phys., vol. 69, pp. 32-47, 1983.
2. L. M. Pecora and T. L. Carroll, "Synchronization in chaotic system," Phys. Rev. Lett., vol. 64, pp. 821-824, 1990.
3. M. J. Ogorzalek, "Taming chaos - Part I: Synchronization," IEEE Trans. Circuits Syst. II, vol. 40, pp. 693-699, Oct. 1993.
4. L. M. Pecora, T. L. Carroll, G. A. Johnson, and D. J. Mar, "Fundamentals of synchronization in chaotic systems, concepts, and applications," Chaos, vol. 7, pp. 520-543, 1997.
5. K. Otsuka, J. L. Chern, and J. S. Lih, "Experimental suppression of chaos in a modulated multimode laser," Opt. Lett., vol. 22, pp. 292-294, 1997.
6. G. Heidari-Bateni and C. D. McGillem, "A chaotic direct-sequence spread spectrum communication system," IEEE Trans. Commun., vol. 42, pp. 1524-1527, Feb./Mar./Apr. 1994.
7. M. P. Kennedy and H. Dedieu, "Synchronization of dynamical systems: Recent progress, potential application and limitations," in Proc. NSIP'95, 1995, pp. 121-124.
8. G. Kolumbán, M. P. Kennedy, and L. O. Chua, "The role of synchronization in digital communications using chaos - Part I: Fundamentals of digital communications," IEEE Trans. Circuits Syst. I, vol. 44, pp. 927-9936, Oct. 1997.
9. M. P. Kennedy, H. Dedieu, and M. Hasler, "Chaos shift keying: Modulation and demodulation of a chaotic carrier using self-synchronising Chua's circuits," IEEE Trans. Circuits Syst. II, vol. 40, pp. 634-642, Oct. 1993.
10. U. Parlitz, L. O. Chua, Lj. Kocarev, K. S. Halle, and A. Shang, "Transmission of digital signals by chaotic synchronization," Int. J. Bifurc. Chaos, vol. 2, pp. 973-977, 1992.
11. J. Schweizer, M. P. Kennedy, M. Hasler, and H. Dedieu, "Synchronization theorem for a chaotic system," Int. J. Bifurc. Chaos, vol. 5, pp. 297-302, 1995.
12. R. He and P. G. Vaidya, "Analysis and synthesis of synchronous periodic and chaotic system," Phys. Rev. A, vol. 46, pp. 7387-7392, 1992.
13. T. Kapitaniak, M. Sekieta, and M. Orgorzalek, "Monotone synchronization of chaos," Int. J. Bifurc. Chaos, vol. 6, pp. 211-217, 1996.
14. R. Brown and N. F. Rulkov, "Synchronization of chaotic systems: Transverse stability of trajectories in invariant manifolds," Chaos, vol. 7, pp. 395-413, 1997.
15. P. Ashwin, J. Buescu, and I. Stewart, "From attractor to chaotic saddle: A tale of transverse instability," Nonlinearity, vol. 9, pp. 703-737, 1996.
16. E. Ott and J. C. Sommerer, "Blowout bifurcations: The occurrence of riddled basins and on-off intermittency," Phys. Lett. A, vol. 188, pp. 39-47, 1994.
17. J. F. Heagy, T. L. Carroll, and L. M. Pecora, "Desynchronization by periodic orbits," Phys. Rev. E, vol. 52, pp. R1253-1256, 1995.
18. D. J. Gauthier and J. C. Bienfang, "Intermittent loss of synchronization in coupled chaotic oscillators: Toward a new criterion for high-quality synchronization," Phys. Rev. Lett, vol. 77, pp. 1751-1754, 1996.
19. M. M. Sushchik, Jr., N. F. Rulkov, and H. D. I. Abarbanel, "Robustness and stability of synchronized chaos: An illustrative model," IEEE Trans. Circuits Syst. I, vol. 44, pp. 867-873, Oct. 1997.
20. Y. M. Liaw and P. C. Tung, "Analysis and observer design in synchronization via a state feedback control method," Phys. Rev. E, vol. 56, pp. 5265-5271, 1997.
21. R. Brown and N. F. Rulkov, "Synchronization of chaotic systems: The effect of additive noise and drift in the dynamics of the driving," Phys. Rev. E, vol. 50, pp. 4488-4508, 1994.
22. R. Brown, N. F. Rulkov, and E. R. Tracy, "Modeling and synchronizing chaotic systems from time series data," Phys. Rev. E., vol. 49, pp. 3784-3800, 1994.
23. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, 1984.
24. A. Lasota and M. C. Mackey, Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics, 2nd ed. New York: Springer-Verlag, 1994.
25. G. Golub and G. Watson, Matrix Computations. Baltimore, MD: The Johns Hopkins Press, 1983.
26. J. M. Greene and J. S. Kim, "The calculation of Lyapunov spectra," Physica D, vol. 24, pp. 213-221, 1987.
27. H. D. I. Abarbanel, R. Brown, J. L. Sidorowich, and L. S. Tsimring, "The analysis of observed chaotic data in physical systems," Rev. Mod. Phys., vol. 65, pp. 1331-1392, 1993.
28. H. D. I. Abarbanel, R. Brown, and M. B. Kennel, "Variation of Lyapunov exponents on a strange attractor," J. Nonlinear Sci., vol. 1, pp. 175-199, 1991.