From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators

Physica D: Nonlinear Phenomena

Volumn 143, Issue 1-4, 2000, Pages 1-20

  Strogatz, Steven H ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

Coupled oscillators; Kinetic theory; Kuramoto model; Plasma physics

Indexed keywords

EID: 0039592729     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(00)00094-4     Document Type: Article

References (60)

1. Crawford J.D. J. Statist. Phys. 74:1994;1047.
2. Crawford J.D. Phys. Rev. Lett. 74:1995;4341.
3. Crawford J.D., Davies K.T.R. Physica D. 125:1999;1.
4. Y. Kuramoto, in: H. Arakai (Ed.), International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, Vol. 39, Springer, New York, 1975, p. 420.
5. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Springer, Berlin, 1984.
6. Kuramoto Y. Progr. Theoret. Phys. Suppl. 79:1984;223.
7. Sakaguchi H., Kuramoto Y. Progr. Theoret. Phys. 76:1986;576.
8. Kuramoto Y., Nishikawa I. J. Statist. Phys. 49:1987;569.
9. Y. Kuramoto, I. Nishikawa, in: H. Takayama (Ed.), Cooperative Dynamics in Complex Physical Systems, Springer, Berlin, 1989.
10. Winfree A.T. J. Theoret. Biol. 16:1967;15.
11. A.T. Winfree, The Geometry of Biological Time, Springer, New York, 1980.
12. S.H. Strogatz, I. Stewart, Sci. Am. 269 (6) (1993) 102.
13. S.H. Strogatz, in: S. Levin (Ed.), Frontiers in Mathematical Biology, Lecture Notes in Biomathematics, Vol. 100, Springer, New York, 1994, p. 122.
14. C.S. Peskin, Mathematical Aspects of Heart Physiology, Courant Institute of Mathematical Science Publication, New York, 1975, pp. 268-278.
15. Michaels D.C., Matyas E.P., Jalife J. Circulation Res. 61:1987;704.
16. Liu C., Weaver D.R., Strogatz S.H., Reppert S.M. Cell. 91:1997;855.
17. Ghosh A.K., Chance B., Pye E.K. Arch. Biochem. Biophys. 145:1971;319.
18. Aldridge J., Pye E.K. Nature. 259:1976;670.
19. Buck J. Quart. Rev. Biol. 63:1988;265.
20. Buck J., Buck E. Scientific Am. 234:1976;74.
21. Walker T.J. Science. 166:1969;891.
22. Jiang Z., McCall M. J. Opt. Soc. Am. 10:1993;155.
23. Kourtchatov S.Yu., Likhanskii V.V., Napartovich A.P., Arecchi F.T., Lapucci A. Phys. Rev. A. 52:1995;4089.
24. York R.A., Compton R.C. IEEE Trans. Microwave Theory Tech. 39:1991;1000.
25. Wiesenfeld K., Colet P., Strogatz S.H. Phys. Rev. Lett. 76:1996;404.
26. Wiesenfeld K., Colet P., Strogatz S.H. Phys. Rev. E. 57:1998;1563.
27. N. Wiener, Nonlinear Problems in Random Theory, MIT Press, Cambridge, MA, 1958.
28. N. Wiener, Cybernetics, 2nd Edition, MIT Press, Cambridge, MA, 1961.
29. P. Glansdorff, I. Prigogine, Thermodynamic Theory of Structure, Stability, and Fluctuations, Wiley, London, 1971.
30. Daido H. J. Phys. 20:1987;L629.
31. Daido H. Progr. Theoret. Phys. 81:1989;727.
32. Daido H. Progr. Theoret. Phys. Suppl. 99:1989;288.
33. Daido H. J. Statist. Phys. 60:1990;753.
34. Strogatz S.H., Mirollo R.E. J. Statist. Phys. 63:1991;613.
35. Sakaguchi H. Progr. Theoret. Phys. 79:1988;39.
36. Mirollo R.E., Strogatz S.H. J. Statist. Phys. 60:1990;245.
37. Strogatz S.H., Mirollo R.E., Matthews P.C. Phys. Rev. Lett. 68:1992;2730.
38. Landau L. J. Phys. USSR. 10:1946;25.
39. van Kampen N.G. Physica. 21:1955;949.
40. Case K. Ann. Phys. (NY). 7:1959;349.
41. Weitzner H. Phys. Fluids. 6:1963;1123.
42. H. Weitzner, in: H. Grad (Ed.), Magnetic-Fluid and Plasma Dynamics, American Mathematical Society, Providence, RI, 1967, p. 127.
43. Weitzner H., Dobrott D. Phys. Fluids. 11:1968;1123.
44. E. Infeld, G. Rowlands, Nonlinear Waves, Solitons and Chaos, Cambridge University Press, New York, 1990.
45. Sagan D. Am. J. Phys. 62:1994;450.
46. Crawford J.D., Hislop P.D. Ann. Phys. (NY). 189:1989;265.
47. J.D. Crawford, in: W. Greenberg, J. Polewezak (Eds.), Modern Mathematical Methods in Transport Theory, Operator Theory: Advances and Applications, Vol. 51, Birkhauser, Basel, 1991, p. 97.
48. Crawford J.D. Phys. Rev. Lett. 73:1994;656.
49. Case K. Phys. Fluids. 3:1960;143.
50. Briggs R.J., Daugherty J.D., Levy R.H. Phys. Fluids. 13:1970;421.
51. Churlilov S.M., Shukhman I.G. J. Fluid. Mech. 194:1988;187.
52. Pego R., Weinstein M.I. Philos. Trans. R. Soc. London Ser A. 340:1992;47.
53. Pego R., Smereka P., Weinstein M.I. Nonlinearity. 8:1995;921.
54. Russo G., Smereka P. SIAM. J. Appl. Math. 56:1996;327.
55. M. Reed, B. Simon, Methods of Mathematical Physics, Part IV, Academic Press, New York, 1978.
56. Bonilla L.L., Neu J.C., Spigler R. J. Statist. Phys. 67:1992;313.
57. Daido H. Progr. Theoret. Phys. 88:1992;1213.
58. Daido H. Progr. Theoret. Phys. 89:1993;929.
59. Daido H. Phys. Rev. Lett. 73:1994;760.
60. Daido H. Physica D. 91:1996;24.