Chaos synchronization by resonance of multiple delay times

TL;DR

This paper investigates how resonance of multiple delay times can induce chaos synchronization in networks, extending the GCD rule to multiple delays and analyzing its effects through analytical and numerical methods.

Contribution

It introduces the GCD condition for resonance-induced synchronization in networks with multiple delays, supported by analytical proofs and numerical simulations.

Findings

GCD determines the number of synchronized sublattices in multiple delay networks.

Resonance of delays can induce high correlation even in non-synchronizable networks.

Analytical and numerical results confirm the GCD condition's role in synchronization phenomena.

Abstract

Chaos synchronization may arise in networks of nonlinear units with delayed couplings. We study complete and sublattice synchronization generated by resonance of two large time delays with a specific ratio. As it is known for single delay networks, the number of synchronized sublattices is determined by the Greatest Common Divisor (GCD) of the network loops lengths. We demonstrate analytically the GCD condition in networks of iterated Bernouilli maps with multiple delay times and complement our analytic results by numerical phase diagrams, providing parameter regions showing complete and sublattice synchronization by resonance for Tent and Bernouilli maps. We compare networks with the same GCD with single and multiple delays, and we investigate the sensitivity of the correlation to a detuning between the delays in a network of coupled Stuart-Landau oscillators. Moreover, the GCD condition also allows to detect time delay resonances leading to high correlations in non-synchronizable networks. Specifically, GCD-induced resonances are observed both in a chaotic asymmetric network and in doubly connected rings of delay-coupled noisy linear oscillators.