General framework for phase synchronization through localized sets

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 75, Issue 2, 2007, Pages

  Pereira, T ^a   Baptista, M S ^a   Kurths, J ^a  

^a UNIVERSITY OF POTSDAM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COUPLED CIRCUITS; NEURONS; SYNCHRONIZATION;

COUPLED CHAOTIC OSCILLATORS; INFORMATION EXCHANGE; PHASE SYNCHRONIZATION; SYNCHRONOUS NEURONS;

OSCILLATORS (ELECTRONIC);

EID: 33847654390     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.75.026216     Document Type: Article

References (45)

1. H. Fujisika and T. Yamada, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.69.32 69, 32 (1983).
2. L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.821 64, 821 (1990).
3. L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.2109 80, 2109 (1998).
4. B. Blasius and L. Stone, Nature (London) NATUAS 0028-0836 10.1038/35022646 406, 846 (2000);
5. B. Blasius and L. Stone, Nature (London) NATUAS 0028-0836 10.1038/20676 399, 354 (1999).
6. R. D. Pinto, P. Varona, A. R. Volkovskii, A. Szucs, H. D. I. Abarbanel, and M. I. Rabinovich, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.2644 62, 2644 (2000).
7. M. V. Ivanchenko, G. V. Osipov, V. D. Shalfeev, and J. Kurths, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.134101 93, 134101 (2004).
8. M. Thiel, M. C. Romano, J. Kurths, M. Rolfs, and R. Kliegl, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2006-10147-0 75, 535 (2006).
9. P. De Grauwe, H. Wachter, and M. Embrechts, Exchange Rate Theory: Chaotic Models of Foreign Exchange Markets (Blackwell, Oxford, 1993).
10. I. Leyva, E. Allaria, S. Boccaletti, and F. T. Arecchi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.066209 68, 066209 (2003).
11. I. Fischer, Y. Liu, and P. Davis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.011801 62, 011801 (R) (2000).
12. D. J. DeShazer, R. Breban, E. Ott, and R. Roy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.044101 87, 044101 (2001).
13. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2001);
14. S. Boccaletti, J. Kurths, G. Osipov, D. Valladares, and C. Zhou, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(02)00137-0 366, 1 (2002);
15. J. Kurths, S. Boccaletti, C. Grebogi, Chaos CHAOEH 1054-1500 10.1063/1.1554606 13, 126 (2003).
16. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.1804 76, 1804 (1996);
17. A. S. Pikovsky, M. G. Rosenblum, and J. Kurths, Physica D PDNPDT 0167-2789 76, 1804 (1997).
18. M. S. Baptista and J. Kurths, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.045202 72, 045202 (R) (2005).
19. F. Mormann, T. Kreuz, R. G. Andrzejak, P. David, K. Lehnertz, and C. E. Elger, Epilepsy Res. ZZZZZZ 0920-1211 53, 173 (2003).
20. J. Fell, P. Klaver, C. E. Elger, and G. Fernandez, Rev. Neurosci. ZZZZZZ 0334-1763 13, 299 (2002).
21. U. Parlitz, L. Junge, W. Lauterborn, and L. Kocarev, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.54.2115 54, 2115 (1996).
22. M. S. Baptista, T. P. Silva, J. C. Sartorelli, I. L. Caldas, and E. Rosa, Jr., Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.056212 67, 056212 (2003).
23. I. Z. Kiss and J. L. Hudson, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.046215 64, 046215 (2001).
24. C. M. Ticos, E. Rosa, Jr., W. B. Pardo, J. A. Walkenstein, and M. Monti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.2929 85, 2929 (2000).
25. D. Maraun and J. Kurths, Geophys. Res. Lett. GPRLAJ 0094-8276 10.1029/2005GL023225 32, L15709 (2005).
26. K. Josić and M. Beck, Chaos CHAOEH 1054-1500 10.1063/1.1505812 13, 247 (2003);
27. K. Josić and D. J. Mar, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.056234 64, 056234 (2001).
28. C. Schäfer, M. G. Rosenblum, J. Kurths, and H.-H. Abel, Nature (London) NATUAS 0028-0836 10.1038/32567 392, 239 (1998).
29. M. S. Baptista, T. Pereira, J. C. Sartorelli, I. L. Caldas, and J. Kurths, Physica D PDNPDT 0167-2789 10.1016/j.physd.2005.10.003 212, 216 (2005).
30. R. Quian Quiroga, A. Kraskov, T. Kreuz, and P. Grassberger, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.041903 65, 041903 (2002).
31. E. R. Kandel, J. H. Schwartz, and T. M. Jessel, Principles of Neural Science, 4th ed. (Mc-Graw Hill, New York, 2000).
32. J. L. Hindmarsh and R. M. Rose, Proc. R. Soc. London, Ser. B PRLBA4 0962-8452 221, 87 (1984);
33. J. L. Hindmarsh and R. M. Rose, Nature (London) NATUAS 0028-0836 10.1038/296162a0 296, 162 (1982).
34. S. W. Johnson, V. Seutin, and R. A. North, Science SCIEAS 0036-8075 58, 665 (1992).
35. C. Mulle, A. Madariaga, and M. Deschenes, J. Neurosci. JNRSDS 0270-6474 6, 2134 (1986).
36. A. Destexhe, Z. F. Mainen, and T. J. Sejnowski, Neural Comput. NEUCEB 0899-7667 6, 14 (1994);
37. A. A. Sharp, F. K. Skinner, and E. Narder, J. Neurophysiol. JONEA4 0022-3077 76, 867 (1996).
38. I. N. Sneddon, Fourier Transforms (Dover, New York, 1995).
39. I. Belykh, E. de Lange, and M. Hasler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.188101 94, 188101 (2005).
40. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos (Springer, New York, 1996).
41. S. Hayes, C. Grebogi, E. Ott, and A. Mark, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73.1781 73, 1781 (1994).
42. T. Yalçinkaya and Y. C. Lai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.3885 79, 3885 (1997).
43. R. Borisyuk, G. Borisyuk, and Y. Kazanovich, Behav. Brain Sci. BBSCDH 0140-525X 21, 833 (1998).
44. C. E. Shannon, Bell Syst. Tech. J. BSTJAN 0005-8580 27, 623 (1948).
45. L. S. Pontryagin, Ordinary Differential Equations (Addison-Wesley, New York, 1969).