Transition to intermittent chaotic synchronization

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

Volumn 72, Issue 3, 2005, Pages

  Zhao, Liang ^a,b   Lai, Ying Cheng ^c,d   Shih, Chih Wen ^d  

^a ARIZONA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

^c Arizona State University   (United States)

^d NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE DURATIONS; LORENZ SYSTEM; LYAPUNOV EXPONENTS; PERIODIC ORBITS;

CHAOS THEORY; ELECTRON TRANSITIONS; FINITE DIFFERENCE METHOD; GEOMETRY; LYAPUNOV METHODS; OSCILLATIONS; THEOREM PROVING;

SYNCHRONIZATION;

EID: 28844443511     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.036212     Document Type: Article

References (28)

1. H. Fujisaka and T. Yamada, Prog. Theor. Phys. PTPKAV 0033-068X 69, 32 (1983);
2. H. Fujisaka and T. Yamada, Prog. Theor. Phys. PTPKAV 0033-068X 75, 1087 (1986);
3. T. Yamada and H. Fujisaka, Prog. Theor. Phys. PTPKAV 0033-068X 70, 1240 (1983);
4. T. Yamada and H. Fujisaka, Prog. Theor. Phys. PTPKAV 0033-068X 72, 885 (1984).
5. V. S. Afraimovich, N. N. Verichev, and M. I. Rabinovich, Izv. Vyssh. Uchebn. Zaved., Radiofiz. IVYRAY 0021-3462 29, 1050 (1986);
6. A. R. Volkovskii and N. F. Rul'kov, Sov. Tech. Phys. Lett. STPLD2 0360-120X 15, 249 (1989).
7. L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.821 64, 821 (1990).
8. W. L. Ditto and K. Showalter, Chaos CHAOEH 1054-1500 10.1063/1.166276 7, 509 (1997).
9. J. Kurths, S. Boccaletti, C. Grebogi, and Y.-C. Lai, Chaos CHAOEH 1054-1500 10.1063/1.1554606 13, 126 (2003).
10. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization-A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, England, 2001).
11. J. F. Heagy, T. L. Carroll, and L. M. Pecora, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.50.1874 50, 1874 (1994);
12. J. F. Heagy, T. L. Carroll, and L. M. Pecora, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.52.R1253 52, R1253 (1995).
13. J. Rössler, Phys. Lett. PYLAAG 0375-9601 10.1016/0375-9601(76)90101-8 57A, 397 (1976).
14. E. N. Lorenz, J. Atmos. Sci. JAHSAK 0022-4928 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 20, 130 (1963).
15. D. Auerbach, P. Cvitanović, J.-P. Eckmann, G. Gunaratne, and I. Procaccia, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.58.2387 58, 2387 (1987);
16. G. H. Gunaratne and I. Procaccia, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.59.1377 59, 1377 (1987);
17. D. Auerbach, B. O'Shaughnessy, and I. Procaccia, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.37.2234 37, 2234 (1988).
18. Y.-C. Lai, C. Grebogi, J. A. Yorke, and S. C. Venkataramani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.55 77, 55 (1996).
19. P. Ashwin, J. Biescu, and I. Stewart, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(94)90947-4 193, 126 (1994).
20. S. C. Venkataramani, B. R. Hunt, E. Ott, D. J. Gauthier, and J. C. Bienfang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.5361 77, 5361 (1996);
21. A. V. Zimin, B. R. Hunt, and E. Ott, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.016204 67, 016204 (2003).
22. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.1804 76, 1804 (1996).
23. J. D. Farmer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.47.179 47, 179 (1981).
24. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.4193 78, 4193 (1997).
25. C. Sparrow, The Lorenz Equations: Bifurcations, Chaos and Strange Attractors (Springer-Verlag, New York, 1982).
26. Z. Liu, Y.-C. Lai, and M. A. Matias, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.045203 67, 045203 (R) (2003);
27. Y.-C. Lai and Z. Liu, Chaos CHAOEH 1054-1500 10.1063/1.1637735 14, 189 (2004).
28. R. L. Davidchack and Y.-C. Lai, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.6172 60, 6172 (1999).