The onset of synchronization in systems of globally coupled chaotic and periodic oscillators

Physica D: Nonlinear Phenomena

Volumn 173, Issue 1-2, 2002, Pages 29-51

  Ott, Edward ^a   So, Paul ^b   Barreto, Ernest ^b   Antonsen, Thomas ^a  

^a The Institute for Research in Electronics and Applied Physics   (United States)

^b GEORGE MASON UNIVERSITY   (United States)

Author keywords

Chaos; Coupled oscillators; Kuramoto model; Synchronization

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; MATHEMATICAL MODELS; STABILITY;

PERIODIC OSCILLATORS;

SYNCHRONIZATION;

EID: 0036888198     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(02)00663-2     Document Type: Article

References (23)

1. Y. Kuramoto, in: H. Araki (Ed.), Proceedings of the International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, vol. 39, Springer, Berlin, 1975; Y. Kuramoto, Chemical Oscillators, Waves and Turbulence, Springer, Berlin, 1984.
2. Y. Kuramoto, in: H. Araki (Ed.), Proceedings of the International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, vol. 39, Springer, Berlin, 1975; Y. Kuramoto, Chemical Oscillators, Waves and Turbulence, Springer, Berlin, 1984.
3. A.T. Winfree, The Geometry of Biological Time, Springer, New York, 1980.
4. Strogatz S.H., Mirollo R.E., Matthews P.C., Phys. Rev. Lett. 68 1992 2730.
5. Ermentrout B., J. Math. Biol. 29 1991 571.
6. Acebron J.A., Bonilla L.L., Spigler R., Phys. Rev. E 62 2000 3437.
7. Yeung M.K.S., Strogatz S.H., Phys. Rev. Lett. 82 1999 648.
8. Kozyreff G., Vladimorov A.G., Mandel P., Phys. Rev. Lett. 895 2000 3809.
9. Ramana Reddy D.V., Sen A., Johnston G.L., Phys. Rev. Lett. 80 1998 5109.
10. Frank T.D., Daffertshofer A., Peper C.E., Beek P.J., Haken H., Physica D 150 2001 219.
11. Strogatz S.H., Physica D 143 2000 1.
12. Walker T.J., Science 166 1969 891.
13. Buck J., Q. Rev. Biol. 63 1988 265.
14. Wiesenfeld K., Colet P., Strogatz S.H., Phys. Rev. Lett. 76 1996 404.
15. C.S. Peskin, Mathematical Aspects of Heart Physiology, Courant Institute of Mathematical Sciences, New York, 1975.
16. Pikovsky A.S., Rosenblum M.G., Kurths J., Europhys. Lett. 34 1996 165.
17. Sakaguchi H., Phys. Rev. E 61 2000 7212.
18. Topaj D., Kye W.-H., Pikovsky A., Phys. Rev. Lett. 87 2001 074101.
19. E. Ott, Chaos in Dynamical Systems, Cambridge University Press, Cambridge, 1993, Chapter 3.
20. N.A. Krall, A.W. Trivelpiece, Principles of Plasma Physics, McGraw-Hill, New York, 1973, Section 8.7 T.H. Stix, Theory of Plasma Waves, American Institute of Physics, New York, 1992.
21. N.A. Krall, A.W. Trivelpiece, Principles of Plasma Physics, McGraw-Hill, New York, 1973, Section 8.7 T.H. Stix, Theory of Plasma Waves, American Institute of Physics, New York, 1992.
22. J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer, New York, 1983, Section 3.4.
23. Barreto E., Hunt B.R., Grebogi C., Yorke J.A., Phys. Rev. Lett. 78 1997 4561.