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.
Original language | English |
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Article number | 022206 |
Journal | Physical Review E |
Volume | 93 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Feb 2016 |
Externally published | Yes |