Algebraic relaxation of an order parameter in randomly coupled limit-cycle oscillators

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

Volumn 61, Issue 2, 2000, Pages 2145-2147

  Daido, Hiroaki ^a  

^a KYUSHU INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE SIZE EFFECT; INTEGRATION SCHEME; INTRINSIC FREQUENCY; LIMIT-CYCLE OSCILLATORS; ORDER PARAMETER; POWER-LAW BEHAVIOR; RANDOMLY COUPLED;

OSCILLATORS (ELECTRONIC);

EID: 0000815996     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.2145     Document Type: Article

References (18)

1. A.T. Winfree, The Geometry of Biological Time (Springer, New York, 1980).
2. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984).
3. For a collection of recent papers, see H. Daido Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, 807 (1997).
4. A. K. Engel , Trends Neurosci. 15, 218 (1992).
5. H. Daido, Prog. Theor. Phys. 77, 622 (1987).
6. H. Daido, Phys. Rev. Lett. 68, 1073 (1992).
7. Note that the original variables in Eq. (2) of Ref. 6 are here transformed as (Formula presented) (Formula presented).
8. D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975).
9. Similar results were obtained later for a Lorentzian distribution of (Formula presented) as well [H. Daido (unpublished)].
10. A correction: The time axis in Fig. 5(a) of Ref. 6 should read (Formula presented).
11. Although the notation (Formula presented) is not used in Ref. 6, its content is included in the explanation of Fig. 5 (left column, p. 1075) and its caption.
12. One may consider (Formula presented) instead of (Formula presented), but by self-averaging, both quantities will probably become equal to each other in the limit (Formula presented). A reason for choosing the latter is that it is expected to be analytically more tractable than the former.
13. J. C. Stiller and G. Radons, Phys. Rev. E 58, 1789 (1998).
14. L. L. Bonilla, C. J. Pérez Vicente, and J. M. Rubí, J. Stat. Phys. 70, 921 (1993)
15. S. Uchiyama and H. Fujisaka, Phys. Rev. E 56, 99 (1997)
16. Phys. Rev. EK. Park, S. W. Rhee, and M. Y. Choi, 57, 5030 (1998)
17. T. Aonishi, K. Kurata, and M. Okada, Phys. Rev. Lett. 82, 2800 (1999).
18. H. Daido, J. Stat. Phys. 60, 753 (1990).