Control and synchronization of space extended dynamical systems

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 11, Issue 11, 2001, Pages 2715-2729

  Bragard, J ^a   Boccaletti, S ^b   Arecchi, F T ^c  

^a NORTHEASTERN UNIVERSITY   (United States)

^b UNIVERSITY OF NAVARRA   (Spain)

^c ISTITUTO NAZIONALE DI OTTICA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035516391     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127401003796     Document Type: Review

References (59)

1. Aranson, I., Levine, H. & Tsimring, L. [1994] "Controlling spatio-temporal chaos," Phys. Rev. Lett. 72, 2561-2564.
2. Arecchi, F. T., Boccaletti, S., Ramazza, P. L. & Residori, S. [1993] "Transition from boundary to bulk controlled regimes in optical pattern formation," Phys. Rev. Lett. 70, 2277-2280.
3. Auerbach, D., Cvitanovic, P., Eckmann, J.-P., Gunaratne, G. & Procaccia, I. [1987] "Exploring chaotic motion through periodic orbits," Phys. Rev. Lett. 58, 2387-2389.
4. Bleich, M. E., Hochheiser, D., Moloney, J. V. & Socolar, E. S. [1997] "Controlling extended systems with spatially filtered, time-delayed feedback," Phys. Rev. E55, 2119-2126.
5. Boccaletti, S. & Arecchi, F. T. [1995] "Adaptive control of chaos," Europhys. Lett. 31, 127-132.
6. Boccaletti, S., Maza, D., Mancini, H., Genesio, R. & Arecchi, F. T. [1997a] "Control of defects and space-like structures in delayed dynamical systems," Phys. Rev. Lett. 79, 5246-5249.
7. Boccaletti, S., Farini, A., Kostelich, E. J. & Arecchi, F. T. [1997b] "Adaptive targeting of chaos," Phys. Rev. E55, R4845-R4848.
8. Boccaletti, S., Farini, A. & Arecchi, F. T. [1997c] "Adaptive synchronization of chaos for secure communication," Phys. Rev. E55, 4979-4981.
9. Boccaletti, S., Giaquinta, A. & Arecchi, F. T. [1997d] "Adaptive recognition and filtering of noise using wavelets," Phys. Rev. E55, 5393-5397.
10. Boccaletti, S., Bragard, J., Arecchi, F. T. & Mancini, H. L. [1999] "Synchronization in non-identical extended systems," Phys. Rev. Lett. 83, 536-539.
11. Boccaletti, S., Grebogi, C., Lai, Y. C., Mancini, H. & Maza, D. [2000] "The control of chaos: Theory and applications," Phys. Rep. 329, 103-197.
12. Boccaletti, S. & Valladares, D. L. [2000] "Characterization of intermittent lag synchronization," Phys. Rev. E62, 7497-7500.
13. Chaté, H. [1994] "Spatiotemporal intermittency regimes of the one-dimensional complex Ginzburg-Landau equation," Nonlinearity 7, 185-204.
14. Chaté, H., Pikovsky, A. & Rudzick, O. [1999] "Forcing oscillatory media: Phase kinks vs. synchronization," Physica (Amsterdam) D113, 17-30.
15. Coullet, P., Gil, L. & Roca, F. [1989] "Optical vortices," Opt. Commun. 73, 403-408.
16. Cross, M. & Hohenberg, P. C. [1993] "Pattern formation out of equilibrium," Rev. Mod. Phys. 65, 851-1112.
17. Cuomo, K. M. & Oppenheim, A. V. [1993] "Circuit implementation of synchronized chaos with applications to communications," Phys. Rev. Lett. 71, 65-68.
18. Ditto, W. L., Rauseo, S. N. & Spano, M. L. [1990] "Experimental control of chaos," Phys. Rev. Lett. 65, 3211-3214.
19. Egolf, D. & Greenside, H. [1994] "Relation between fractal dimension and spatial correlation length for extensive chaos," Nature (London) 369, 129-131.
20. Femat, R. & Solis-Perales, G. [1999] "On the chaos synchronization phenomena," Phys. Lett. A262, 50-60.
21. Gershenfeld, N. & Grinstein, G. [1995] "Entrapment and communication with dissipative pseudorandom dynamics," Phys. Rev. Lett. 74, 5024-5027.
22. Grigoriev, R. O., Cross, M. C. & Schuster, H. G. [1997] "Pinning control of spatiotemporal chaos," Phys. Rev. Lett. 79, 2795-2798.
23. Hayes, S., Grebogi, C., Ott, E. & Mark, A. [1994] "Experimental control of chaos for communication," Phys. Rev. Lett. 73, 1781-1784.
24. Hochheiser, D., Moloney, J. V. & Lega, J. [1997] "Controlling optical turbulence," Phys. Rev. A55, R4011-R4014.
25. Hunt, E. R. [1991] "Stabilizing high-period orbits in a chaotic system: The diode resonators," Phys. Rev. Lett. 67, 1953-1955.
26. Janiaud, B., Pumir, A., Bensimon, D., Croquette, V., Richter, H. & Kramer, L. [1992] "The Eckaus instability for travelling waves," Physica (Amsterdam) D55, 269-286.
27. Junge, L. & Parlitz, U. [2000] "Phase synchronization of coupled Ginzburg-Landau equations," Phys. Rev. E62, 438-441.
28. Kocarev, L. & Parlitz, U. [1995] "General approach for chaotic synchronization with applications to communications," Phys. Rev. Lett. 74, 5028-5031.
29. Kocarev, L. & Parlitz, U. [1996] "Generalized synchronization, predictability and equivalence of unidirectionally coupled dynamical systems," Phys. Rev. Lett. 76, 1816-1819.
30. Kolodner, P., Slimani, S., Aubry, N. & Lima, R. [1995] "Characterization of dispersive chaos and related states of binary fluid convection," Physica (Amsterdam) D85, 165-224.
31. Kuramoto, Y. & Koga, S. [1981] "Turbulized rotating chemical waves," Prog. Theor. Phys. Suppl. 66, 1081-1085.
32. Leweke, T. & Provansal, M. [1994] "Model for the transition in bluff body wakes," Phys. Rev. Lett. 72, 3174-3177.
33. Lu, W., Yu, D. & Harrison, R. G. [1996] "Control of patterns in spatiotemporal chaos in optics," Phys. Rev. Lett. 76, 3316-3319.
34. Martin, R., Scroggie, A. J., Oppo, G.-L. & Firth, W. J. [1996] "Stabilization, selection and tracking of unstable patterns by Fourier space techniques," Phys. Rev. Lett. 77, 4007-4010.
35. Meucci, R., Gadomski, W., Ciofini, M. & Arecchi, F. T. [1994] "Experimental control of chaos by means of weak parametric perturbations," Phys. Rev. E49, R2528-R2531.
36. Meucci, R., Ciofini, M. & Abbate, R. [1996] "Suppressing chaos in lasers by negative feedback," Phys. Rev. E53, R5537-R5540.
37. Montagne, R., Hernández-García, E. & San Miguel, M. [1996] "Winding number instability in the phase-turbulence regime of the complex Ginzburg-Landau equation," Phys. Rev. Lett. 77, 267-270.
38. Montagne, R. & Colet, P. [1997] "Nonlinear diffusion control of spatiotemporal chaos in the complex Ginzburg-Landau equation," Phys. Rev. E56, 4017-4024.
39. Neiman, A., Pei, X., Russell, D., Wojtenek, W., Wilkens, L., Moss, F., Braun, H. A., Huber, M. T. & Voigt, K. [1999] "Synchronization of the noisy electrosensitive cells in the paddlefish," Phys. Rev. Lett. 82, 660-663.
40. Ott, E., Grebogi, C. & Yorke, J. A. [1990] "Controlling chaos," Phys. Rev. Lett. 64, 1196-1199.
41. Parmananda, P., Hildebrand, M. & Eiswirth, M. [1997a] "Controlling turbulence in coupled map lattice systems using feedback techniques," Phys. Rev. E56, 239-244.
42. Parmananda, P. [1997b] "Generalized synchronization of spatiotemporal chemical chaos," Phys. Rev. E56, 1595-1598.
43. Pecora, L. M. & Carroll, T. L. [1990] "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824.
44. Peng, J. H., Ding, E. J., Ding, M. & Yang, W. [1996] "Synchronizing hyperchaos with a scalar transmitted signal," Phys. Rev. Lett. 76, 904-907.
45. Petrov, V., Gaspar, V., Masere, J. & Showalter, K. [1993] "Controlling chaos in the Belousov-Zhabotinsky reaction," Nature 361, 240-243.
46. Pyragas, K. [1992] "Continuous control of chaos by self-controlling feedback," Phys. Lett. A170, 421-428.
47. Rosa, E., Jr., Ott, E. & Hess, M. H. [1998] "Transition to phase synchronization of chaos," Phys. Rev. Lett. 80, 1642-1645.
48. Rosenblum, M. G., Pikovsky, A. S. & Kurths, J. [1996] "Phase synchronization of chaotic oscillators," Phys. Rev. Lett. 76, 1804-1807.
49. Rosenblum, M. G., Pikovsky, A. S. & Kurths, J. [1997] "From phase to lag synchronization in coupled chaotic oscillators," Phys. Rev. Lett. 78, 4193-4196.
50. Roy, R., Murphy, T. W., Jr., Maier, T. D., Gills, Z. & Hunt, E. R. [1992] "Dynamical control of chaotic laser: Experimental stabilization of a globally coupled system," Phys. Rev. Lett. 68, 1259-1262.
51. 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. E51, 980-994.
52. Sakaguchi, H. [1990] "Breakdown of the phase dynamics," Prog. Theor. Phys. 84, 792-800.
53. Schafer, C., Rosemblum, M. G., Kurths, J. & Abel, H. H. [1998] "Heartbeat synchronized with ventilation," Nature 392, 239-240.
54. Shraiman, B., Pumir, A., van Saarloos, W., Hohenberg, P. C., Chate, H. & Holen, M. [1992] "Spatiotemporal chaos in the one-dimensional complex Ginzburg-Landau equation," Physica (Amsterdam) D57, 241-248.
55. Tass, P., Rosenblum, M. G., Weule, M. G., Kurths, J., Pikovsky, A., Volkmann, J., Schnitzler, A. & Freund, H. J. [1998] "Detection of n : m phase locking from noisy data: Application to magneto-encephalography," Phys. Rev. Lett. 81, 3291-3294.
56. Torcini, A. [1996] "Order parameter for the transition from phase to amplitude turbulence," Phys. Rev. Lett. 77, 1047-1050.
57. van Hecke, M. [1998] "Building blocks of spatiotemporal intermittency," Phys. Rev. Lett. 80, 1896-1899.
58. Van Wiggeren, G. D. & Roy, R. [1998] "Communication with chaotic lasers," Science 279, 1198-1200.
59. Zaks, M. A., Park, E.-H., Rosenblum, M. G. & Kurths, J. [1999] "Alternating locking ratios in imperfect phase synchronization," Phys. Rev. Lett. 82, 4228-4231.