Abstract
An exact solution to a model of mutually interacting sinusoidal oscillators is found. Limits on the variation of the native frequencies are determined in order for synchronization to occur. These limits are computed for different distributions of native frequencies.
Similar content being viewed by others
References
Aizawa, Y.: Synergetic approach to the phenomena of mode-locking in nonlinear systems. Prog. Theor. Phys. 56, 703–716 (1976)
Cohen, A. H., Holmes, P. J., Rand, R. H.: The nature of coupling between sequential oscillators of the lamprey spinal generator. J. Math. Biol. 13, 345–369 (1982)
Ermentrout, G. B., Kopell, N.: Frequency plateaus in a chain of weakly coupled oscillators. I. SIAM J. Math. Anal. 15, 215–237 (1984)
Ermentrout, G. B., Kopell, N.: (1984) (Preprint.)
Kuramoto, Y.: Self-entrainment of a population of coupled non-linear oscillators, In: “Mathematical Problems in Theoretical Physics”, Araki, H, ed. Berlin, Heidelberg, New York, Springer, p. 420. (1975)
Neu, J. C.: Large populations of coupled chemical oscillations. SIAM J. Appl. Math. 38, 305–316 (1979)
Winfree, A. T.: The Geometry of Biological Time, Berlin, Heidelberg, New York, Springer, Chapter 4 (1980)
Author information
Authors and Affiliations
Additional information
This research was supported by NSF Award No. MCS8300885 and the Alfred Sloan Foundation.
Rights and permissions
About this article
Cite this article
Ermentrout, G.B. Synchronization in a pool of mutually coupled oscillators with random frequencies. J. Math. Biology 22, 1–9 (1985). https://doi.org/10.1007/BF00276542
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00276542