Journal of Mathematical Biology

, Volume 22, Issue 1, pp 1–9 | Cite as

Synchronization in a pool of mutually coupled oscillators with random frequencies

  • G. Bard Ermentrout


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.

Key words

Oscillations phaselocking phase models all-to-all coupling 


  1. 1.
    Aizawa, Y.: Synergetic approach to the phenomena of mode-locking in nonlinear systems. Prog. Theor. Phys. 56, 703–716 (1976)Google Scholar
  2. 2.
    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)Google Scholar
  3. 3.
    Ermentrout, G. B., Kopell, N.: Frequency plateaus in a chain of weakly coupled oscillators. I. SIAM J. Math. Anal. 15, 215–237 (1984)Google Scholar
  4. 4.
    Ermentrout, G. B., Kopell, N.: (1984) (Preprint.)Google Scholar
  5. 5.
    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)Google Scholar
  6. 6.
    Neu, J. C.: Large populations of coupled chemical oscillations. SIAM J. Appl. Math. 38, 305–316 (1979)Google Scholar
  7. 7.
    Winfree, A. T.: The Geometry of Biological Time, Berlin, Heidelberg, New York, Springer, Chapter 4 (1980)Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • G. Bard Ermentrout
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of PittsburghPittsburghUSA

Personalised recommendations