Synchronization between adaptively coupled systems with discrete and distributed time-delays

IEEE Transactions on Automatic Control

Volumn 55, Issue 4, 2010, Pages 819-830

  Lin, Wei ^a,b   Ma, Huanfei ^a  

^a FUDAN UNIVERSITY   (China)

^b MAX PLANCK INSTITUTE   (Germany)

Author keywords

Adaptive coupling; Control; Locally Lipschitzian; Synchronization; Time delays

Indexed keywords

ADAPTIVE COUPLING; COMPLETE SYNCHRONIZATION; COMPLEX NETWORKS; COUPLED SYSTEMS; CRITICAL VALUE; DISCRETE AND DISTRIBUTED DELAYS; DISTRIBUTED TIME; DISTRIBUTED TIME DELAYS; EXPONENTIAL CONVERGENCE RATE; KINETIC SYSTEMS; LIPSCHITZ; LIPSCHITZ CONDITIONS; LIPSCHITZIAN; LOCAL LIPSCHITZ CONDITION; SYNCHRONIZATION TIME; TIME VARYING; TIME-DELAYED SYSTEMS; VECTOR FIELDS;

TIME DELAY;

SYNCHRONIZATION;

EID: 77950849323     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2041993     Document Type: Article

References (34)

1. M. Bennett, M. F. Schatz, H. Rockwood, and K. Wiesenfeld, "Huygens' clocks," Proc. R. Soc. Lond. A, vol.458, pp. 563-579, 2002.
2. S. H. Strogatz, "Exploring complex networks," Nature, vol.410, pp. 268-276, 2001.
3. S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, "The synchronization of chaotic systems," Phys. Rep., vol.366, pp. 1-101, 2002.
4. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge, U.K.: Cambridge Univ. Press, 2001.
5. P. F. Hokayem and M. W. Spong, "Bilateral teleoperation: An historical survey," Automatica, vol.42, pp. 2035-2057, 2006.
6. H. Fujisaka and T. Yamada, "Stability theory of synchronized motion in coupled-oscillator systems," Prog. Theor. Phys., vol.69, pp. 32-43, 1983.
7. C. W. Wu and L. O. Chua, "Synchronization in an array of linearly coupled dynamical systems," IEEE Trans. Circuits Syst. I, vol.42, no.8, pp. 430-447, Aug. 1995.
8. G. Chen and X. Dong, From Chaos to Order: Methodologies, Persperctives and Applications. Singapore: World Scientific, 1998.
9. K. M. Cuomo, A. V. Oppenheim, and S. H. Stogatz, "Synchronization of Lorenz based chaotic circuits with applications to communications," IEEE Trans. Circuits Syst. II, vol.40, no.10, pp. 626-633, Oct. 1993.
10. H. Dedieu and M. J. Ogorzalek, "Identifiability and identification of chaotic systems based on adaptive synchronization," IEEE Trans. Circuits Syst. I, vol.44, no.10, pp. 948-962, Oct. 1997.
11. Z. H. Guan, G. Chen, X. Yu, and Y. Qin, "Robust decentralized stablization for a cloass of large-scale time-delay uncertain impulsive dynamical systems," Automatica, vol.38, pp. 2075-2084, 2002.
12. C. S. Zhou and J. Kurths, "Noise-induced phase synchronization and synchronization transitions in chaotic oscillators," Phys. Rev. Lett., vol.88, p. 230602, 2002.
13. W. Lin and G. Chen, "Using white noise to enhance synchronization of coupled chaotic systems," Chaos, vol.16, p. 013134, 2006.
14. W. Lin, "Realization of synchronization in time-delayed systems with stochastic perturbation," J. Phys. A: Math. Theor., vol.41, p. 235101, 2008.
15. K. Lian, P. Liu, T. Chiang, and C. Chiu, "Adaptive synchronization design for chaotic systems via a scalar driving signal," IEEE Trans. Circuits Syst. I, vol.49, no.1, pp. 17-27, Jan. 2002.
16. D. Sun, "Position synchronization of multiple motion axes with adaptive coupling control," Automatica, vol.39, pp. 997-1005, 2003.
17. W. Lin and H. F. Ma, "Failure of parameter identification based on adaptive synchronization techniques," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol.75, p. 066212, 2007.
18. J. Zhou, J. Lu, and J. Lü, "Adaptive synchronization of an uncertain complex dynamical network," IEEE Trans. Autom. Control, vol.51, no.4, pp. 652-656, Apr. 2006.
19. J. Zhou, J. Lu, and J. Lü, "Pinning adaptive synchronization of a general complex dynamical network," Automatica, vol.44, pp. 996-1003, 2008.
20. C. Sparrow, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. New York: Springer-Verlag, 1982.
21. J. Lü, G. Chen, and S. Celikovsky, "Bridge the gap between the Lorenz system and the Chen sytem," Int. J. Bifur. Chaos, vol.12, pp. 2917-2926, 2002.
22. O. E. Rössler, "An equation for continuous chaos," Phys. Lett. A, vol.57, pp. 397-398, 1976.
23. J. Vano, J. Wildenberg, M. Anderson, J. Noel, and J. Sprott, "Chaos in low-dimensional Lotka-Volterra models of competition," Nonlinearity, vol.19, pp. 2391-2404, 2006.
24. W. Lin, "Adaptive chaos control and synchronization in only locally Lipschitz systems," Phys. Lett. A, vol.372, pp. 3195-13120, 2008.
25. J. Hale and S. M. V. Lunel, Introduction to Functional Differential Equations. New York: Springer-Verlag, 1993.
26. V.Kolmanovskii and A. Myshkis, Applied Theory of Functional Differential Equations. London, U.K.: Kluwer Academic Publishers, 1992.
27. E.-K. Boukas and Z. Liu, Deterministic and Stochastic Time-Delay Systems. New York: Springer-Verlag, 2002.
28. K. Wang, Z. Teng, and H. Jiang, "Adaptive synchronization of neural networks with time-varying delay and distributed delay," Physica A, vol.387, pp. 631-642, 2008.
29. J. Lu, J. Cao, and D. W. C. Ho, "Adaptive stabilization and synchronization for chaotic Lur'e systems with time-varying delay," IEEE Trans. Circuits Syst. I, vol.55, no.5, pp. 1347-1356, Jun. 2008.
30. N. Chopra, M. W. Spong, and R. Lozano, "Synchronization of bilateral teleoperators with time delay," Automatica, vol.44, pp. 2142-2148, 2008.
31. K. Yoshida, Functional Analysis. New York: Springer-Verlag, 1980.
32. J. Hale, Theory of Functional Differential Equations. New York: Springer-Verlag, 2003.
33. T. Yoshizawa, Stability Theory and Existence of Periodic Solutions and Almost Periodic Solutions. New York: Springer-Verlag, 1975.
34. J. E. Slotine and W. Li, Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice Hall, 1991.