Clustering in time delay chaotic networks and the greatest common divisor

Ido Kanter, Meital Zigzag, Wolfgang Kinzel

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)52-55
Number of pages4
JournalIEICE Proceedings Series
Issue numberA1L-D1
StatePublished - 4 Sep 2011


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