Extending anticipation horizon of chaos synchronization schemes with time-delay coupling

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 368, Issue 1911, 2010, Pages 305-317

  Pyragas, Kestutis ^a,b   Pyragiene, Tatjana ^a  

^a CENTER FOR PHYSICAL SCIENCES AND TECHNOLOGY   (Lithuania)

^b VILNIUS UNIVERSITY   (Lithuania)

Author keywords

Anticipating synchronization of chaos; Coupling design; Time delay feedback

Indexed keywords

SYNCHRONIZATION; TIME DELAY;

ANTICIPATING SYNCHRONIZATION; ANTICIPATING SYNCHRONIZATION OF CHAOS; CHAOS SYNCHRONIZATION; CHAOTIC OSCILLATION; COUPLING LAW; COUPLING MATRIX; DESIGN TIME; DYNAMICAL MODEL; PHASE LAGS; PREDICTION HORIZON; ROSSLER SYSTEM; SLAVE SYSTEMS; TIME-DELAY COUPLING;

CHAOTIC SYSTEMS;

ALGORITHM; ARTICLE; ELECTRONICS; NONLINEAR SYSTEM; OSCILLOMETRY; STATISTICAL MODEL; SYSTEMS THEORY; TIME;

ALGORITHMS; ELECTRONICS; MODELS, STATISTICAL; NONLINEAR DYNAMICS; OSCILLOMETRY; SYSTEMS THEORY; TIME FACTORS;

EID: 76149089248     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2009.0211     Document Type: Article

References (30)

1. Afraimovich, V. S., Verichev, N. N. & Rabinovich, M. I. 1986 Stochastically synchronized oscillations in dissipative systems. Izv. Vyssh. Uchebn. Zaved. Radiofiz. 29, 1050-1060.
2. Boccaletti, S., Kurths, J., Osipov, G., Valladares, D. L. & Zhou, C. S. 2002 The synchronization of chaotic systems. Phys. Rep. 366, 1-101. (doi:10.1016/S0370-1573(02)00137-0)
3. Calvo, O., Chialvo, D. R., Eguiluz, V. M., Mirasso, C. & Toral, R. 2004 Anticipated synchronization: a metaphorical linear view. Chaos 14, 7-13. (doi:10.1063/1.1620991) (Pubitemid 38430231)
4. Ciszak, M., Calvo, O., Masoller, C., Mirasso, C. & Toral, R. 2003 Anticipating the response of excitable systems driven by random forcing. Phys. Rev. Lett. 90, 204 102. (doi:10.1103/PhysRevLett.90.204102)
5. Ciszak, M., Marino, F., Toral, R. & Balle, S. 2004 Dynamical mechanism of anticipating synchronization in excitable systems. Phys. Rev. Lett. 93, 114 102. (doi:10.1103/PhysRevLett.93.114102)
6. Ciszak, M., Gutierrez, M., Cofino, A. S., Mirasso, C., Toral, R., Pesquera, L. & Ortin, S. 2005 Approach to predictability via anticipated synchronization. Phys. Rev. E 72, 046 218. (doi:10.1103/PhysRevE.72.046218)
7. Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J. & Knuth, D. E. 1996 On the Lambert W function. Adv. Comput. Math. 5, 329-359. (doi:10.1007/BF02124750)
8. Fiedler, B., Flunkert, V., Georgi, M., Hovel, P. & Scholl, E. 2007 Refuting the odd-number limitation of time-delayed feedback control. Phys. Rev. Lett. 98, 114 101. (doi:10.1103/PhysRevLett.98.114101) (Pubitemid 46434099)
9. Gauthier, D. J., Sukow, D. W., Concannon, H. M. & Socolar, J. E. S. 1994 Stabilizing unstable periodic orbits in a fast diode resonator using continuous time-delay autosynchronization. Phys. Rev. E 50, 2343-2346. (doi:10.1103/PhysRevE.50.2343)
10. Kostur, M., Hanggi, P., Talkner, P. & Mateos, J. L. 2005 Anticipated synchronization in coupled inertial ratchets with time-delayed feedback: a numerical study. Phys. Rev. E 72, 036 210. (doi:10.1103/PhysRevE.72.036210)
11. Mainieri, R. & Rehacek, J. 1999 Projective synchronization in three-dimensional chaotic systems. Phys. Rev. Lett. 82, 3042-3045. (doi:10.1103/PhysRevLett.82.3042)
12. Masoller, C. 2001 Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback. Phys. Rev. Lett. 86, 2782-2785. (doi:10.1103/PhysRevLett.86.2782) (Pubitemid 32293385)
13. Mendoza, C., Boccaletti, S. & Politi, A. 2004 Convective instabilities of synchronization manifolds in spatially extended systems. Phys. Rev. E 69, 047 202. (doi:10.1103/PhysRevE.69.047202)
14. Pecora, L. M. & Carroll, T. L. 1990 Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821-824. (doi:10.1103/PhysRevLett.64.821)
15. Pikovsky, A., Rosemblum, M. & Kurths, J. 2001 Synchronization: a universal concept in nonlinear sciences. Cambridge, UK: Cambridge University Press.
16. Pyragas, K. 1992 Continuous control of chaos by self-controlling feedback. Phys. Lett. A 170, 421-428. (doi:10.1016/0375-9601(92)90745-8)
17. Pyragas, K. 1995 Control of chaos via extended delay feedback. Phys. Lett. A 206, 323-330. (doi:10.1016/0375-9601(95)00654-L)
18. Pyragas, K. 1996 Weak and strong synchronization of chaos. Phys. Rev. E 54, R4508-R4512. (doi:10.1103/PhysRevE.54.R4508)
19. Pyragas, K. 1998 Synchronization of coupled time-delay systems: analytical estimations. Phys. Rev. E 58, 3067-3071. (doi:10.1103/PhysRevE.58. 3067)
20. Pyragas, K. 2006 Delayed feedback control of chaos. Phil. Trans. R. Soc. A 364, 2309-2334. (doi:10.1098/rsta.2006.1827) (Pubitemid 44328172)
21. Pyragas, K. & Pyragien?e, T. 2008 Coupling design for a long-term anticipating synchronization of chaos. Phys. Rev. E 78, 046 217. (doi:10.1103/PhysRevE.78.046217)
22. Rosenblum, M. G., Pikovsky, A. S. & Kurths, J. 1996 Phase synchronization of chaotic oscillators. Phys. Rev. Lett. 76, 1804-1807. (doi:10.1103/PhysRevLett.76.1804)
23. Rosenblum, M. G., Pikovsky, A. S. & Kurths, J. 1997 From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett. 78, 4193-4196. (doi:10.1103/PhysRevLett.78.4193) (Pubitemid 127655459)
24. Rossler, O. E. 1976 An equation for continuous chaos. Phys. Lett. A 57, 397-398. (doi:10.1016/0375-9601(76)90101-8)
25. Rulkov, N. F., Sushchik, M. M., Tsimring, L. S. & Abarbanel, H. D. I. 1995 Generalized synchronization of chaos in directionally coupled chaotic systems. Phys. Rev. E 51, 980-994. (doi:10.1103/PhysRevE.51.980)
26. Sivaprakasam, S., Shahverdiev, E. M., Spencer, P. S. & Shore, K. A. 2001 Experimental demonstration of anticipating synchronization in chaotic semiconductor lasers with optical feedback. Phys. Rev. Lett. 87, 154 101. (doi:10.1103/PhysRevLett.87.154101)
27. Tang, S. & Liu, J. M. 2003 Experimental verification of anticipated and retarded synchronization in chaotic semiconductor lasers. Phys. Rev. Lett. 90, 194 101. (doi:10.1103/PhysRevLett.90.194101)
28. Voss, H. U. 2000 Anticipating chaotic synchronization. Phys. Rev. E 61, 5115-5119. (doi:10.1103/PhysRevE.61.5115)
29. Voss, H. U. 2001 Dynamic long-term anticipation of chaotic states. Phys. Rev. Lett. 87, 014 102. (doi:10.1103/PhysRevLett.87.014102)
30. Voss, H. U. 2002 Real-time anticipating of chaotic states of an electronic circuit. Int. J. Bifurc. Chaos Appl. Sci. Eng. 12, 1619-1625. (doi:10.1142/S0218127402005340)