title: 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.
authors.affiliation: Departamento Fisica Fundamental, Universidad Nacional Educación a Distancia, C/ Senda del Rey 9, 28040 Madrid, Spain.
authors.forename: Manuel Jimenez
authors.initials: MJ
authors.lastname: Martin
authors.affiliation: Department of Physics, Duke University, Box 90305, 120 Science Drive, Durham, North Carolina 27708, USA.|Institute of Theoretical Physics, University of Würzburg, Am Hubland, 97074 Würzburg, Germany.
authors.forename: Otti
authors.initials: O
authors.lastname: D'Huys
authors.affiliation: Institute of Theoretical Physics, University of Würzburg, Am Hubland, 97074 Würzburg, Germany.
authors.forename: Laura
authors.initials: L
authors.lastname: Lauerbach
authors.affiliation: Departamento Fisica Fundamental, Universidad Nacional Educación a Distancia, C/ Senda del Rey 9, 28040 Madrid, Spain.|Georgi Nadjakov Institute of Solid State Physics, Bulgarian Academy of Sciences, 1784, Sofia, Bulgaria.
authors.forename: Elka
authors.initials: E
authors.lastname: Korutcheva
authors.affiliation: Institute of Theoretical Physics, University of Würzburg, Am Hubland, 97074 Würzburg, Germany.
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Kinzel