Journal of Mathematical Biology

, Volume 29, Issue 6, pp 571–585 | Cite as

An adaptive model for synchrony in the firefly Pteroptyx malaccae

  • B. Ermentrout


We describe a new model for synchronization of neuronal oscillators that is based on the observation that certain species of fireflies are able to alter their free-running period. We show that by adding adaptation to standard oscillator models it is possible to observe the frequency alteration. One consequence of this is the perfect synchrony between coupled oscillators. Stability and some analytic results are included along with numerical simulations.

Key words

Fireflies Synchronization Nonlinear oscillations 


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  1. 1.
    Buck, J.: Synchronous rhythmic flashing in fireflies. II., Q. Rev. Biol. 63, 265–289 (1988)Google Scholar
  2. 2.
    Buck J., Buck E., Hanson F., Case, J. F., Mets, L., Atta, G. J.: Control of flashing in fireflies. IV, Free run pacemaking in a synchronic Pteroptyx. J. Comp. Physiol. 144, 277–286 (1981)Google Scholar
  3. 3.
    Ermentrout, G. B.: Synchronization in a pool of mutually coupled oscillators with random frequencies, J. Math. Biology 22, 1–9 (1985)Google Scholar
  4. 4.
    Glass, L., Perez, R.: Fine structure of phaselocking. Phys. Rev. Letters, 48, 1772–1775 (1982)Google Scholar
  5. 5.
    Hanson, F. E.: Comparative studies of firefly pacemakers. Fed. Proc. 37, 2158–2164 (1978)Google Scholar
  6. 6.
    Hanson, F. E.: Pacemaker control of rhythmic flashing of fireflies. In: Carpenter, D. (ed.) Cellular Pacemakers, Vol. 2, pp. 81–100. New York: John Wiley 1982Google Scholar
  7. 7.
    Hoppensteadt, F. C., Keener, J. P.: Phaselocking of biological clocks. J. Math. Biol. 15, 339–346 (1982)Google Scholar
  8. 8.
    Keener, J. P., Glass, L.: Global bifurcations of a periodically forced nonlinear oscillator. J. Math. Biol. 21, 175–190 (1984)Google Scholar
  9. 9.
    Kepler, T., Marder, E., Abbott, L.: The effect of electrical coupling on the frequency of model neuronal oscillators. Science 248, 83–85 (1990)Google Scholar
  10. 10.
    Moore-Ede, M. C., Sulzman, F. M., Fuller, C. A.: The clocks That Time Us. Cambridge: University Press 1982Google Scholar
  11. 11.
    Peskin, C. S.: Mathematical Aspects of Heart Physiology. Courant Inst. of Math. Sci. Publ., NYU 268–278 (1975)Google Scholar
  12. 12.
    Rinzel, J., Ermentrout, G. B.: Beyond a pacemaker's entrainment limit: phase walk-through. Am. J. Physiol. 246, R102–106 (1983)Google Scholar
  13. 13.
    Strogatz, S., Mirollo, R.: Phase-locking and critical phenomena in lattices of coupled nonlinear oscillators with random intrinsic frequencies. Physica 31D, 143–168 (1988)Google Scholar
  14. 14.
    Strogatz, S., Mirollo, R.: Synchronization of pulse coupled biological oscillators. SIAM J. Appl. Math. 50, 1645–1662 (1990)Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • B. Ermentrout
    • 1
  1. 1.Department of MathematicsUniversity of PittsburghPittsburghUSA

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