- 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

Dynamical robustness of coupled heterogeneous oscillators

Gouhei Tanaka1,2,4, Kai Morino2, Hiroaki Daido3, and Kazuyuki Aihara1,2,4

  • 1Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
  • 2Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
  • 3Graduate School of Engineering, Osaka Prefecture University, Sakai 599-8531, Japan
  • 4Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan

PDF

Phys. Rev. E 89, 052906 – Published 12 May, 2014

DOI: https://doi.org/10.1103/PhysRevE.89.052906

Abstract

We study tolerance of dynamic behavior in networks of coupled heterogeneous oscillators to deterioration of the individual oscillator components. As the deterioration proceeds with reduction in dynamic behavior of the oscillators, an order parameter evaluating the level of global oscillation decreases and then vanishes at a certain critical point. We present a method to analytically derive a general formula for this critical point and an approximate formula for the order parameter in the vicinity of the critical point in networks of coupled Stuart-Landau oscillators. Using the critical point as a measure for dynamical robustness of oscillator networks, we show that the more heterogeneous the oscillator components are, the more robust the oscillatory behavior of the network is to the component deterioration. This property is confirmed also in networks of Morris-Lecar neuron models coupled through electrical synapses. Our approach could provide a useful framework for theoretically understanding the role of population heterogeneity in robustness of biological networks.

View figure in article

Article Text

References (33)

  1. A. L. Barabási and Z. N. Oltvai, Nat. Rev. Genet. 5, 101 (2004).
  2. H. Kitano, Nat. Rev. Genet. 5, 826 (2004).
  3. J. M. Carlson and J. Doyle, Proc. Natl. Acad. Sci. USA 99, 2538 (2002).
  4. H. Kitano, Mol. Syst. Biol. 3, 137 (2007).
  5. S. H. Strogatz, Nonlinear Dynamics and Chaos (Perseus, Cambridge, MA, 2000).
  6. A. T. Winfree, The Geometry of Biological Time, 2nd ed. (Springer, New York, 2001).
  7. H. Daido and K. Nakanishi, Phys. Rev. Lett. 93, 104101 (2004).
  8. D. Pazó and E. Montbrió, Phys. Rev. E 73, 055202(R) (2006).
  9. H. Daido and K. Nakanishi, Phys. Rev. E 75, 056206 (2007).
  10. G. Tanaka, Y. Okada, and K. Aihara, Phys. Rev. E 82, 035202(R) (2010).
  11. H. Daido, Europhys. Lett. 84, 10002 (2008).
  12. K. Morino, G. Tanaka, and K. Aihara, Phys. Rev. E 83, 056208 (2011).
  13. G. Tanaka, K. Morino, and K. Aihara, Sci. Rep. 2, 232 (2012).
  14. Z. He, S. Liu, and M. Zhan, Physica A 392, 4181 (2013).
  15. K. Morino, G. Tanaka, and K. Aihara, Phys. Rev. E 88, 032909 (2013).
  16. S. Bernard, D. Gonze, B. Čajavec, H. Herzel, and A. Kramer, PLoS Comput. Biol. 3, 0667 (2007).
  17. D. K. Welsh, J. S. Takahashi, and S. A. Kay, Annu. Rev. Physiol. 72, 551 (2010).
  18. N. Geva-Zatorsky, N. Rosenfeld, S. Itzkovitz, R. Milo, A. Sigal, E. Dekel, T. Yarnitzky, Y. Liron, P. Polak, G. Lahav et al., Mol. Syst. Biol. 2, 2006.0033 (2006).
  19. G. Buzsáki and A. Draguhn, Science 304, 1926 (2004).
  20. H. Daido, Phys. Rev. E 84, 016215 (2011).
  21. H. Daido, A. Kasama, and K. Nishio, Phys. Rev. E 88, 052907 (2013).
  22. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Tokyo,1984).
  23. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, Berlin, 1983).
  24. P. Erdős and A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960).
  25. R. Pastor-Satorras and A. Vespignani, Phys. Rev. Lett. 86, 3200 (2001).
  26. A. L. Barabási and R. Albert, Science 286, 509 (1999).
  27. C. Morris and H. Lecar, Biophys. J. 35, 193 (1981).
  28. K. Tsumoto, H. Kitajima, T. Yoshinaga, K. Aihara, and H. Kawakami, Neurocomp. 69, 293 (2006).
  29. J. Rinzel and G. B. Ermentrout, in Methods in Neuronal Modeling, edited by C. Koch and I. Segev (MIT Press, Cambridge, MA, 1989), pp. 135–169.
  30. P. Balenzuela and J. Garciá-Ojalvo, Phys. Rev. E 72, 021901 (2005).
  31. D. Golomb and J. Rinzel, Phys. Rev. E 48, 4810 (1993).
  32. A. S. Pikovsky, M. G. Rosenblum, and J. Kurths, Europhys. Lett. 34, 165 (1996).
  33. J. Hasenauer, S. Waldherr, M. Doszczak, N. Radde, P. Scheurich, and F. Allgöwer, BMC Bioinf. 12, 125 (2011).

Outline

Information

Phys. Rev. E 89, 052906– Published 12 May, 2014
  • Received 3 September 2013
  • Revised 1 April 2014

©2014 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation