- 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

Traveling echo waves in an array of excitable elements with time-delayed coupling

Oriol Vallès-Codina1,2, Ronny Möbius2, Sten Rüdiger2, and Lutz Schimansky-Geier2

  • 1IBE-Institut de Biologia Evolutiva (UPF/CSIC), Barcelona, Spain
  • 2Institut für Physik, Humboldt-Universität zu Berlin, Germany

PDF

Phys. Rev. E 83, 036209 – Published 23 March, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.036209

Abstract

We study time-delayed coupling in one-dimensional arrays of discrete excitable FitzHugh-Nagumo elements. For small time delays in an excitatory coupling, noise-triggered spikes undergo a slight prolongation. For larger delay times, the coupling to adjacent elements leads to a splitting of spikes and an “echo” effect that produces dampened series of spikes. For very large delay times, a transition to a stationary regime appears, as the spikes are sustained by mutual excitations, resulting in antiphase synchronization of all elements. We characterize several features exhibited by the system, such as speed and duration of pulses as well as bifurcations leading to the stationary regime.

View figure in article

Article Text

References (23)

  1. B. Lindner, J. García-Ojalvo, A. Neiman, and L. Schimansky-Geier, Phys. Rep. 392, 321 (2004).
  2. F. Sagués, J. M. Sancho, and J. García-Ojalvo, Rev. Mod. Phys. 79, 829 (2007).
  3. R. A. FitzHugh, Biophys. J. 1, 445 (1961).
  4. J. Nagumo, S. Arimoto, and S. Yoshitzawa, Proc. IRE 50, 2061 (1962).
  5. E. Alvarez-Lacalle and E. Moses, J. Comput. Neurosci. 26, 475 (2009).
  6. S. Rüdiger and L. Schimansky-Geier, J. Theor. Biol. 259, 96 (2009).
  7. M. Falcke, Adv. Phys. 53, 255 (2004).
  8. S. Zeller, S. Rüdiger, H. Engel, J. Sneyd, G. Warnecke, I. Parker, and M. Falcke, Biophys. J. 97, 992 (2009).
  9. S. Rüdiger, C. Nagaiah, G. Warnecke, and J. W. Shuai, Biophys. J. 99, 3 (2010).
  10. Y.-X. Li and J. Rinzel, J. Theor. Biol. 166, 461 (1994).
  11. L. Meinhold and L. Schimansky-Geier, Phys. Rev. E 66, 050901(R) (2002).
  12. A. Hutt, M. Bestehorn, and T. Wennekers, Netw. Comput. Neural Syst. 14, 351 (2003).
  13. A. Hutt and F. M. Atay, Phys. Rev. E 73, 021906 (2006).
  14. G. Golomb and G. B. Ermentrout, Netw. Comput. Neural Syst. 11, 221 (2000).
  15. H. Haken, Eur. Phys. J. B 18, 545 (2000).
  16. R. Osan and B. Ermentrout, Phys. D 163, 217 (2002).
  17. R. I. Leine and H. Nijmeijer, Dynamics and Bifurcations of Non-Smooth Mechanical Systems (Springer, Berlin, 2004).
  18. J. Hizanidis, A. Balanov, A. Amann, and E. Schöll, Phys. Rev. Lett. 96, 244104 (2006).
  19. N. Buric and D. Todorovic, Phys. Rev. E 67, 066222 (2003).
  20. E. Schöll, G. Hiller, P. Hövel, and M. A. Dahlem, Phil. Trans. R. Soc. A 367, 1079 (2009).
  21. M. A. Dahlem, G. Hiller, A. Panchuk, and E. Schöll, Int. J. Bifur. Chaos 19, 745 (2009).
  22. S. Sailer, D. Hennig, V. Beato, H. Engel, and L. Schimansky-Geier, Phys. Rev. E 73, 056209 (2006).
  23. K. Engelborghs, T. Luzyanina, and D. Roose, ACM Trans. Math. Softw. 28, 1 (2002).

Outline

Information

Phys. Rev. E 83, 036209– Published 23 March, 2011
  • Received 3 March 2010

©2011 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation