- 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

Synchronization of oscillators through time-shifted common inputs

Ehsan Bolhasani1,2, Yousef Azizi1, Alireza Valizadeh1,2, and Matjaž Perc3,4

  • 1Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
  • 2School of Cognitive Science, Institute for Research in Fundamental Sciences (IPM), P.O. Box 1954851167, Tehran, Iran
  • 3Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
  • 4CAMTP–Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia

PDF

Phys. Rev. E 95, 032207 – Published 9 March, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.032207

Abstract

Shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems. However, due to finite signal transmission speeds and differences in the distance to the source, time shifts between otherwise common inputs are unavoidable. Since common inputs can be a source of correlation between the elements of multi-unit dynamical systems, regardless of whether these elements are directly connected with one another or not, it is of importance to understand their impact on synchronization. As a canonical model that is representative for a variety of different dynamical systems, we study limit-cycle oscillators that are driven by stochastic time-shifted common inputs. We show that if the oscillators are coupled, time shifts in stochastic common inputs do not simply shift the distribution of the phase differences, but rather the distribution actually changes as a result. The best synchronization is therefore achieved at a precise intermediate value of the time shift, which is due to a resonance-like effect with the most probable phase difference that is determined by the deterministic dynamics.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (51)

  1. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept In Nonlinear Sciences (Cambridge University Press, Cambridge, 2003).
  2. S. H. Strogatz, Sync: The Emerging Science of Spontaneous Order (Hyperion, New York, 2003).
  3. F. Blaabjerg, R. Teodorescu, M. Liserre, and A. V. Timbus, IEEE Trans. Ind. Electr. 53, 1398 (2006).
  4. M. Rohden, A. Sorge, M. Timme, and D. Witthaut, Phys. Rev. Lett. 109, 064101 (2012).
  5. A. E. Motter, S. A. Myers, M. Anghel, and T. Nishikawa, Nat. Phys. 9, 191 (2013).
  6. P. Barbara, A. B. Cawthorne, S. V. Shitov, and C. J. Lobb, Phys. Rev. Lett. 82, 1963 (1999).
  7. K. K. Likharev, Dynamics of Josephson Junctions and Circuits (Gordon & Breach, Philadelphia, 1986).
  8. J. Jalife, J. Physiol. 356, 221 (1984).
  9. C. S. Peskin, Mathematical Aspects of Heart Physiology (Courant Institute of Mathematical Sciences, New York, 1975).
  10. C. M. Gray and W. Singer, Proc. Natl. Acad. Sci. USA 86, 1698 (1989).
  11. M. I. Rabinovich, R. Huerta, and P. Varona, Phys. Rev. Lett. 96, 014101 (2006).
  12. M. Besserve, S. C. Lowe, N. K. Logothetis, B. Schölkopf, and S. Panzeri, PLoS Biol. 13, e1002257 (2015).
  13. L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990).
  14. N. F. Rulkov, M. M. Sushchik, L. S. Tsimring, and H. D. I. Abarbanel, Phys. Rev. E 51, 980 (1995).
  15. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996).
  16. A. Neiman, L. Schimansky-Geier, A. Cornell-Bell, and F. Moss, Phys. Rev. Lett. 83, 4896 (1999).
  17. S. Boccaletti, J. Kurths, G. Osipov, D. Valladares, and C. Zhou, Phys. Rep. 366, 1 (2002).
  18. A. Arenas, A. Díaz-Guilera, and C. J. Pérez-Vicente, Phys. Rev. Lett. 96, 114102 (2006).
  19. A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou, Phys. Rep. 469, 93 (2008).
  20. I. Fischer, R. Vicente, J. M. Buldú, M. Peil, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, Phys. Rev. Lett. 97, 123902 (2006).
  21. J. Gómez-Gardenes, Y. Moreno, and A. Arenas, Phys. Rev. Lett. 98, 034101 (2007).
  22. J. Gómez-Gardenes, S. Gómez, A. Arenas, and Y. Moreno, Phys. Rev. Lett. 106, 128701 (2011).
  23. J. Aguirre, R. Sevilla-Escoboza, R. Gutiérrez, D. Papo, and J. M. Buldú, Phys. Rev. Lett. 112, 248701 (2014).
  24. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, New York, 1984).
  25. K. Pyragas, Phys. Rev. E 58, 3067 (1998).
  26. M. K. S. Yeung and S. H. Strogatz, Phys. Rev. Lett. 82, 648 (1999).
  27. W. S. Lee, E. Ott, and T. M. Antonsen, Phys. Rev. Lett. 103, 044101 (2009).
  28. Q. Wang, M. Perc, Z. Duan, and G. Chen, Phys. Rev. E 80, 026206 (2009).
  29. S. Sadeghi and A. Valizadeh, J. Comput. Neurosci. 36, 55 (2014).
  30. M. Dhamala, V. K. Jirsa, and M. Ding, Phys. Rev. Lett. 92, 074104 (2004).
  31. Z. G. Esfahani, L. L. Gollo, and A. Valizadeh, Sci. Rep. 6, 23471 (2016).
  32. A. Pototsky and N. B. Janson, Phys. Rev. E 80, 066203 (2009).
  33. M. K. Sen, B. C. Bag, K. G. Petrosyan, and C.-K. Hu, J. Stat. Mech. (2010) P08018.
  34. O. D'Huys, T. Jüngling, and W. Kinzel, Phys. Rev. E 90, 032918 (2014).
  35. D. S. Goldobin and A. Pikovsky, Physica A 351, 126 (2005).
  36. J.-N. Teramae and D. Tanaka, Phys. Rev. Lett. 93, 204103 (2004).
  37. A. S. Pikovsky, Phys. Lett. A 165, 33 (1992).
  38. L. Yu, E. Ott, and Q. Chen, Phys. Rev. Lett. 65, 2935 (1990).
  39. B. Hauschildt, N. B. Janson, A. Balanov, and E. Schöll, Phys. Rev. E 74, 051906 (2006).
  40. Y. Kawamura and H. Nakao, Phys. Rev. E 94, 032201 (2016).
  41. E. Bolhasani, Y. Azizi, and A. Valizadeh, Front. Comput. Neurosci. 7, 108 (2013).
  42. A. T. Winfree, The Geometry of Biological Time (Springer, New York, 1980).
  43. G. B. Ermentrout and N. Kopell, J. Math. Biol. 29, 195 (1991).
  44. E. M. Izhikevich, Dynamical Systems in Neuroscience (MIT Press, Cambridge, MA, 2007).
  45. W. Gerstner, Phys. Rev. Lett. 76, 1755 (1996).
  46. D. Hansel and G. Mato, Phys. Rev. Lett. 86, 4175 (2001).
  47. S. H. Strogatz, Nature (London) 410, 268 (2001).
  48. P. Tass, M. G. Rosenblum, J. Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, and H.-J. Freund, Phys. Rev. Lett. 81, 3291 (1998).
  49. S. D. Burton, G. B. Ermentrout, and N. N. Urban, J. Neurophysiol. 108, 2115 (2012).
  50. S. Boccaletti, G. Bianconi, R. Criado, C. I. Del Genio, J. Gómez-Gardeñes, M. Romance, I. Sendiña-Nadal, Z. Wang, and M. Zanin, Phys. Rep. 544, 1 (2014).
  51. M. Kivelä, A. Arenas, M. Barthelemy, J. P. Gleeson, Y. Moreno, and M. A. Porter, J. Complex Netw. 2, 203 (2014).

Outline

Information

Phys. Rev. E 95, 032207– Published 9 March, 2017
  • Received 14 November 2016

©2017 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation