Three coupled oscillators as a universal probe of synchronization stability in coupled oscillator arrays

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 61, Issue 5, 2000, Pages 5080-5090

  Fink, Kenneth S ^a   Johnson, Gregg ^b   Carroll, Tom ^b   Mar, Doug ^b   Pecora, Lou ^b  

^a Columbia University ^*  (United States)

^b NAVAL RESEARCH LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

OSCILLATORS (ELECTRONIC); OSCILLATORS (MECHANICAL); PROBES;

COUPLED OSCILLATOR ARRAY; COUPLED OSCILLATORS; SYNCHRONIZATION STABILITY;

SYNCHRONIZATION;

EID: 0000540384     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.5080     Document Type: Article

References (39)

1. H. Fujisaka and T. Yamada, Prog. Theor. Phys. 69, 32 (1983).
2. V. S. Afraimovich, N. N. Verichev, and M. I. Rabinovich, Izv. Vyssh. Uchebn. Zaved. Radio Fiz. 29, 795–803 (1986).
3. A. R. Volkovskii and N. F. Rul’kov, Sov. Tech. Phys. Lett. 15, 249 (1989).
4. J. M. Kowalski, G. L. Albert, and G. W. Gross, Phys. Rev. A 42, 6260 (1990).
5. J. F. Heagy, T. L. Carroll, and L. M. Pecora, Phys. Rev. E 50, 1874 (1994).
6. H. G. Winful and L. Rahman, Phys. Rev. Lett. 65, 1575 (1990).
7. P. Ashwin, J. Buescu, and I. Stewart, Phys. Lett. A 193, 126 (1994).
8. J. F. Heagy, T. L. Carroll, and L. M. Pecora, Phys. Rev. Lett. 73, 3528 (1994).
9. J. F. Heagy, T. L. Carroll, and L. M. Pecora, Phys. Rev. E 52, R1253 (1995).
10. D. J. Gauthier and J. C. Bienfang, Phys. Rev. Lett. 77, 1751 (1996).
11. A. S. Pikovskii, Radiophys. Quantum Electron. 27, 390 (1984).
12. N. Kopell and G. B. Ermentrout, Math. Biosci. 90, 87 (1988).
13. Y. Kuramoto, in International Symposium on Mathematical Problems in Theoretical Physics, edited by H. Araki, Lecture Notes in Physics Vol. 39 (Springer, Berlin, 1975), pp. 420–422.
14. S. Watanabe and S. H. Strogatz, Phys. Rev. Lett. 70, 2391 (1993).
15. Steven Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley Publishing Co., Reading Massachusettes, 1994).
16. S. H. Strogatz, in Frontiers in Mathematical Biology, edited by S. Levin (Springer, New York, 1994), Vol. 100, pp. 122–138.
17. Chai Wah Wu and Leon O. Chua, Int. J. Bifurcation Chaos Appl. Sci. Eng. 4, 979 (1994).
18. C. W. Wu and L. O. Chua, IEEE Trans. Circuits Syst. 42, 430 (1995).
19. C. W. Wu and L. O. Chua, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 43, 161 (1996).
20. D. Armbruster and G. Dangelmayr, Math. Proc. Cambridge Philos. Soc. 101, 167 (1987).
21. M. Golubitsky and I. Stewart, in Multiparameter Bifurcation Theory, Contemporary Mathematics, edited by M. Golubitsky and J. Guckenheimer (American Mathematical Society, Providence, 1986), Vol. 56, pp. 131–173.
22. V. Pérez-Villar , Int. J. Bifurcation Chaos Appl. Sci. Eng. 3, 1067 (1993).
23. P. M. Gade, Phys. Rev. E 54, 64 (1996).
24. P. M. Gade, H. Cerdeira, and R. Ramaswamy, Phys. Rev. E 52, 2478 (1995).
25. Gang Hu, Junzhong Yang, and Winji Liu, Phys. Rev. E 58, 4440 (1998).
26. L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 80, 2109 (1998).
27. L. Pecora, T. Carroll, and J. Heagy (unpublished).
28. N. F. Rulkov and M. M. Sushchik, Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, 625 (1997).
29. G. H. Golub and C. F. Van Loan, Matrix Computations (The Johns Hopkins University Press, Baltimore, MD, 1996).
30. L. M. Pecora , Chaos 7, 520 (1997).
31. L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990).
32. L. M. Pecora and T. L. Carroll, Phys. Rev. A 44, 2374 (1991).
33. T. L. Carroll and L. M. Pecora, IEEE Trans. Circuits Syst. 38, 453 (1991).
34. J. F. Heagy, L. M. Pecora, and T. L. Carroll, Phys. Rev. Lett. 74, 4185 (1995).
35. J. A. Sanders and F. Verhulst, Averaging Methods in Nonlinear Dynamical Systems (Springer-Verlag, New York, 1985).
36. O. E. Rössler, Phys. Lett. A 57, 397 (1976).
37. R. Brown and N. F. Rulkov, Phys. Rev. Lett. 78, 4189 (1997).
38. Similar criteria are used in control theory and are known as frozen Jacobian criteria. See W. L. Brogan, Modern Control Theory (Prentice-Hall, Englewood Cliffs, NJ, 1991).
39. Tomasz Kapitaniak, Int. J. Bifurcation Chaos Appl. Sci. Eng. 6, 211 (1996).