Clustering in time delay chaotic networks and the greatest common divisor

Ido Kanter; Meital Zigzag; Wolfgang Kinzel

doi:10.34385/proc.45.A1L-D1

Clustering in time delay chaotic networks and the greatest common divisor

Ido Kanter, Meital Zigzag, Wolfgang Kinzel

Department of Physics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

We present the interplay between synchronization of coupled chaotic nodes with heterogeneous delays and the greatest common divisor (GCD) of loops composing the graph. In the weak chaos region and for GCD=1 the network is in chaotic zero-lag synchronization (ZLS), whereas for GCD=m > 1 synchronization of m-clusters emerges. ZLS is achievable even in oriented graphs. The role of GCD is a global decision and cannot be deduced from local topological or geometric properties of the network. Results are supported by simulations of chaotic systems, self-consistent and mixing arguments, as well as analytical solutions of Bernoulli maps.

Original language	English
Pages (from-to)	52-55
Number of pages	4
Journal	IEICE Proceedings Series
Volume	45
Issue number	A1L-D1
DOIs	https://doi.org/10.34385/proc.45.A1L-D1
State	Published - 4 Sep 2011

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10.34385/proc.45.A1L-D1

Cite this

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title = "Clustering in time delay chaotic networks and the greatest common divisor",

abstract = "We present the interplay between synchronization of coupled chaotic nodes with heterogeneous delays and the greatest common divisor (GCD) of loops composing the graph. In the weak chaos region and for GCD=1 the network is in chaotic zero-lag synchronization (ZLS), whereas for GCD=m > 1 synchronization of m-clusters emerges. ZLS is achievable even in oriented graphs. The role of GCD is a global decision and cannot be deduced from local topological or geometric properties of the network. Results are supported by simulations of chaotic systems, self-consistent and mixing arguments, as well as analytical solutions of Bernoulli maps.",

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T1 - Clustering in time delay chaotic networks and the greatest common divisor

AU - Kanter, Ido

AU - Zigzag, Meital

AU - Kinzel, Wolfgang

PY - 2011/9/4

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N2 - We present the interplay between synchronization of coupled chaotic nodes with heterogeneous delays and the greatest common divisor (GCD) of loops composing the graph. In the weak chaos region and for GCD=1 the network is in chaotic zero-lag synchronization (ZLS), whereas for GCD=m > 1 synchronization of m-clusters emerges. ZLS is achievable even in oriented graphs. The role of GCD is a global decision and cannot be deduced from local topological or geometric properties of the network. Results are supported by simulations of chaotic systems, self-consistent and mixing arguments, as well as analytical solutions of Bernoulli maps.

AB - We present the interplay between synchronization of coupled chaotic nodes with heterogeneous delays and the greatest common divisor (GCD) of loops composing the graph. In the weak chaos region and for GCD=1 the network is in chaotic zero-lag synchronization (ZLS), whereas for GCD=m > 1 synchronization of m-clusters emerges. ZLS is achievable even in oriented graphs. The role of GCD is a global decision and cannot be deduced from local topological or geometric properties of the network. Results are supported by simulations of chaotic systems, self-consistent and mixing arguments, as well as analytical solutions of Bernoulli maps.

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DO - 10.34385/proc.45.A1L-D1

M3 - مقالة

SN - 2188-5079

VL - 45

SP - 52

EP - 55

JO - IEICE Proceedings Series

JF - IEICE Proceedings Series

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