Nonequilibrium noise in coupled phase oscillators

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

Volumn 60, Issue 6, 1999, Pages 6402-6406

  Reimann, P ^a   Van den Broeck, C ^b   Kawai, R ^c  

^a UNIVERSITY OF AUGSBURG   (Germany)

^b HASSELT UNIVERSITY   (Belgium)

^c UNIVERSITY OF ALABAMA AT BIRMINGHAM   (United States)

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ARTICLE;

EID: 0001551482     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.6402     Document Type: Article

References (17)

1. G. Nicolis and I. Prigogine, Self Organization in Nonequilibrium Systems, edited by C. Vidal and A. Pacault (Springer, Berlin, 1981);Nonequilibrium Dynamics in Chemical Systems, ibid 1981
2. A.T. Winfree, The Geometry of Biological Time (Springer, Berlin, 1980)
3. L. Glass and M.C. Mackey, From Clocks to Chaos (Princeton University Press, Princeton, NJ, 1988).
4. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984);S.H. Strogatz in Frontiers in Mathematical Biology, edited by S. Levine (Springer, Berlin, 1994), and further references therein.
5. Since the unperturbed frequencies (Formula presented) are not required to be large in comparison with the interaction and the noise in (1), a transformation to an effective state-independent noise by “phase-averaging” 2 is not possible in our case. We further note that the factor (Formula presented) in (2) can equivalently be absorbed as “multiplicative noise” (Formula presented) in (1). The latter is to be understood in the physically relevant sense of Stratonovich 5.
6. A. Arenas and C. Vicente, Phys. Rev. E 50, 949 (1994).
7. H. Risken, The Fokker-Planck Equation (Springer, Berlin, 1984).
8. F. Jülicher and J. Prost, Phys. Rev. Lett. 75, 2618 (1995)
9. F. Jülicher, A. Ajdari, and J. Prost, Rev. Mod. Phys. 69, 1269 (1997).
10. K.A. Alekseev , Phys. Rev. Lett. 80, 2669 (1998).
11. P. Reimann, R. Kawai, C. Van den Broeck, and P. Hänggi, Europhys. Lett. 45, 545 (1999).
12. C. Van den Broeck, J.M.R. Parrondo, R. Toral, and R. Kawai, Phys. Rev. E 55, 4084 (1997).
13. Note that Q can be absorbed into the time-scale in (1), thus (Formula presented) depends only on (Formula presented) and (Formula presented)
14. S. Shinomoto and Y. Kuramoto, Prog. Theor. Phys. 75, 1105 (1986)
15. J.A. Acebron, L.L. Bonilla, S. De Leo, and R. Spigler, Phys. Rev. E 57, 5287 (1998).
16. H. Gang, H. Haken, and X. Fagen, Phys. Rev. Lett. 77, 1925 (1996).
17. For (Formula presented) it can be shown rigorously that (Formula presented)