- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Predicting synchrony in heterogeneous pulse coupled oscillators

Sachin S. Talathi*, Dong-Uk Hwang, Abraham Miliotis, Paul R. Carney, and William L. Ditto

  • J. Crayton Pruitt Department of Biomedical Engineering, University of Florida, Gainesville, Florida 32611, USA

  • *sachin.talathi@bme.ufl.edu
PDF

Phys. Rev. E 80, 021908 – Published 11 August, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.021908

Abstract

Pulse coupled oscillators (PCOs) represent an ubiquitous model for a number of physical and biological systems. Phase response curves (PRCs) provide a general mathematical framework to analyze patterns of synchrony generated within these models. A general theoretical approach to account for the nonlinear contributions from higher-order PRCs in the generation of synchronous patterns by the PCOs is still lacking. Here, by considering a prototypical example of a PCO network, i.e., two synaptically coupled neurons, we present a general theory that extends beyond the weak-coupling approximation, to account for higher-order PRC corrections in the derivation of an approximate discrete map, the stable fixed point of which can predict the domain of 1:1 phase locked synchronous states generated by the PCO network.

View figure in article

Article Text

References (28)

  1. Z. Olami, Hans Jacob S. Feder, and K. Christensen, Phys. Rev. Lett. 68, 1244 (1992).
  2. J. Buck and E. Buck, Sci. Am. 234, 74 (1976).
  3. J. Jalife, J. Physiol. 356, 221 (1984).
  4. C. Kirst and M. Timme, e-print arXiv:0812.1786.
  5. R. Mirollo and S. Strogatz, SIAM J. Appl. Math. 50, 1645 (1990).
  6. U. Ernst, K. Pawelzik, and T. Geisel, Phys. Rev. Lett. 74, 1570 (1995).
  7. P. C. Bressloff, S. Coombes, and B. de Souza, Phys. Rev. Lett. 79, 2791 (1997).
  8. A. Winfree, The Geometry of Biological Time, 2nd ed. (Springer Verlag, New York, 2001).
  9. J. Murray, Mathematical Biology (Springer Verlag, Berlin, 1993).
  10. A. J. Preyer and R. J. Butera, Phys. Rev. Lett. 95, 138103 (2005).
  11. R. F. Galan, G. B. Ermentrout, and N. N. Urban, Phys. Rev. Lett. 94, 158101 (2005).
  12. S. Oprisan and C. Canavier, Diff. Eq. 9, 243 (2001).
  13. S. Oprisan, A. Prinz, and C. Canavier, Biophys. J. 87, 2283 (2004).
  14. M. Guevara, A. Shrier, and L. Glass, Am. J. Physiol. Heart Circ. Physiol. 20, H1298 (1986).
  15. C. Canavier, Scholarpedia J. 1, 1332 (2006).
  16. A. Engel and W. Singer, Trends Cogn. Sci. 5, 16 (2001).
  17. T. Mima, T. Oluwatimilehin, T. Hiraoka, and M. Hallett, J. Neurosci. 21, 3942 (2001).
  18. X. Wang and G. Buzsaki, J. Neurosci. 16, 6402 (1996).
  19. H. D. I. Abarbanel and S. S. Talathi, Phys. Rev. Lett. 96, 148104 (2006).
  20. S. Talathi, D. Hwang, and W. Ditto, J. Comput. Neurosci. 25, 262 (2008).
  21. S. S. Talathi, H. D. I. Abarbanel, and W. L. Ditto, Phys. Rev. E 78, 031918 (2008).
  22. C. Acker, N. Kopell, and J. White, J. Comput. Neurosci. 15, 71 (2003).
  23. B. Ermentrout and N. Kopell, SIAM J. Appl. Math. 50, 125 (1990).
  24. M. Bartos, I. Vida, and P. Jonas, Nat. Rev. Neurosci. 8, 45 (2007).
  25. S. Crook, G. Ermentrout, and J. M. Bower, Neural Comput. 10, 837 (1998).
  26. J. Cui, C. Canavier, and R. Butera, J. Neurophysiol. 102, 387 (2009).
  27. S. Maran and C. Canavier, J. Comput. Neurosci. 24, 37 (2008).
  28. J. Kurths, A. Pikovsky, and M. Rosenblum, Synchronization, A Universal Concept in Non-linear Science (Cambridge University Press, Cambridge, England, 2001).

Outline

Information

Phys. Rev. E 80, 021908– Published 11 August, 2009
  • Received 6 February 2009

© 2009 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation