Synchronization of unidirectional time delay chaotic networks and the greatest common divisor

Abstract

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.

7 pages, 5 figures

References in corpus (5)

• Synchronization in complex networks
• Network Synchronization, Diffusion, and the Paradox of Heterogeneity
• Network synchronization: Spectral versus statistical properties
• Effects of the network structural properties on its controllability
• Sublattice synchronization of chaotic networks with delayed couplings

Cited by in corpus (5)

• Control of synchronization patterns in neural-like Boolean networks
• Introduction to Focus Issue: Patterns of Network Synchronization
• Synchronization Patterns: From Network Motifs to Hierarchical Networks
• Embedding the dynamics of a single delay system into a feed-forward ring
• Hierarchy and Polysynchrony in an adaptive network