Journal of Statistical Physics

, Volume 145, Issue 3, pp 713–733

Nonlocal Mechanism for Synchronization of Time Delay Networks

  • Ido Kanter
  • Evi Kopelowitz
  • Roni Vardi
  • Meital Zigzag
  • Dana Cohen
  • Wolfgang Kinzel
Article

DOI: 10.1007/s10955-011-0361-1

Cite this article as:
Kanter, I., Kopelowitz, E., Vardi, R. et al. J Stat Phys (2011) 145: 713. doi:10.1007/s10955-011-0361-1

Abstract

We present the interplay between synchronization of networks with heterogeneous delays and the greatest common divisor (GCD) of loops composing the network. We distinguish between two types of networks; (I) chaotic networks and (II) population dynamic networks with periodic activity driven by external stimuli. For type (I), in the weak chaos region, the units of a chaotic network characterized by GCD=1 are in a chaotic zero-lag synchronization, whereas for GCD>1, the network splits into GCD-clusters in which clustered units are in zero-lag synchronization. These results are supported by simulations of chaotic systems, self-consistent and mixing arguments, as well as analytical solutions of Bernoulli maps. Type (II) is exemplified by simulations of Hodgkin Huxley population dynamic networks with unidirectional connectivity, synaptic noise and distribution of delays within neurons belonging to a node and between connecting nodes. For a stimulus to one node, the network splits into GCD-clusters in which cluster neurons are in zero-lag synchronization. For complex external stimuli, the network splits into clusters equal to the greatest common divisor of loops composing the network (spatial) and the periodicity of the external stimuli (temporal). The results suggest that neural information processing may take place in the transient to synchronization and imply a much shorter time scale for the inference of a perceptual entity.

Keywords

SynchronizationNetworksChaosNeural networks

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Ido Kanter
    • 1
  • Evi Kopelowitz
    • 1
  • Roni Vardi
    • 2
  • Meital Zigzag
    • 1
  • Dana Cohen
    • 2
  • Wolfgang Kinzel
    • 3
  1. 1.Department of PhysicsBar-Ilan UniversityRamat-GanIsrael
  2. 2.Gonda Interdisciplinary Brain Research Center, and the Goodman Faculty of Life SciencesBar-Ilan UniversityRamat-GanIsrael
  3. 3.Institute for Theoretical PhysicsUniversity of Wuerzburg, Am HublandWuerzburgGermany