Synchronization of unidirectional time delay chaotic networks and the greatest common divisor
Minerva Center and Department of Physics, Bar-Ilan University - Ramat-Gan 52900, Israel
2 Institute for Theoretical Physics, University of Wuerzburg - Am Hubland, 97074 Wuerzburg, Germany, EU
Accepted: 21 February 2011
We present the interplay between synchronization of unidirectional coupled chaotic nodes with heterogeneous delays and the greatest common divisor (GCD) of loops composing the oriented graph. In the weak-chaos region and for GCD = 1 the network is in chaotic zero-lag synchronization, whereas for GCD = m > 1 synchronization of m-sublattices emerges. Complete synchronization can be achieved when all chaotic nodes are influenced by an identical set of delays and in particular for the limiting case of homogeneous delays. Results are supported by simulations of chaotic systems, self-consistent and mixing arguments, as well as analytical solutions of Bernoulli maps.
PACS: 05.45.Xt – Synchronization; coupled oscillators / 02.10.Ox – Combinatorics; graph theory
© EPLA, 2011