Nonlocal Mechanism for Synchronization of Time Delay Networks |
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Authors: | Ido Kanter Evi Kopelowitz Roni Vardi Meital Zigzag Dana Cohen Wolfgang Kinzel |
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Institution: | 1.Department of Physics,Bar-Ilan University,Ramat-Gan,Israel;2.Gonda Interdisciplinary Brain Research Center, and the Goodman Faculty of Life Sciences,Bar-Ilan University,Ramat-Gan,Israel;3.Institute for Theoretical Physics,University of Wuerzburg, Am Hubland,Wuerzburg,Germany |
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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. |
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