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Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Sep;90(3):030902. Epub 2014 Sep 30.

Transient scaling and resurgence of chimera states in networks of Boolean phase oscillators.

Author information

1
Department of Physics, Duke University, 120 Science Drive, Durham, North Carolina 27708, USA and Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, Berlin D-10623, Germany.
2
Department of Physics, Duke University, 120 Science Drive, Durham, North Carolina 27708, USA and Supélec, OPTEL Research Group and LMOPS EA-4423, 2 Rue Edouard Belin, Metz F-57070, France.
3
Department of Physics, Duke University, 120 Science Drive, Durham, North Carolina 27708, USA.
4
Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, Berlin D-10623, Germany.

Abstract

We study networks of nonlocally coupled electronic oscillators that can be described approximately by a Kuramoto-like model. The experimental networks show long complex transients from random initial conditions on the route to network synchronization. The transients display complex behaviors, including resurgence of chimera states, which are network dynamics where order and disorder coexists. The spatial domain of the chimera state moves around the network and alternates with desynchronized dynamics. The fast time scale of our oscillators (on the order of 100ns) allows us to study the scaling of the transient time of large networks of more than a hundred nodes, which has not yet been confirmed previously in an experiment and could potentially be important in many natural networks. We find that the average transient time increases exponentially with the network size and can be modeled as a Poisson process in experiment and simulation. This exponential scaling is a result of a synchronization rate that follows a power law of the phase-space volume.

PMID:
25314385
DOI:
10.1103/PhysRevE.90.030902
[Indexed for MEDLINE]

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