Chaos synchronization by resonance of multiple delay times

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 loop lengths. We demonstrate analytically the GCD condition in networks of iterated Bernoulli 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 Bernoulli 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 detection of time-delay resonances, leading to high correlations in nonsynchronizable networks. Specifically, GCD-induced resonances are observed both in a chaotic asymmetric network and in doubly connected rings of delay-coupled noisy linear oscillators.