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

Abstract

We study networks of non-locally 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 timescale of our oscillators (on the order of $100\mathrm{ns}$) 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.

http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.030902

References in corpus (4)

• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Observation and characterization of chimera states in coupled dynamical systems with nonlocal coupling
• Control of synchronization patterns in neural-like Boolean networks
• Ultra-Fast Physical Generation of Random Numbers Using Hybrid Boolean Networks

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• Detecting partial synchrony in a complex oscillatory network using pseudo-vortices
• Structured scale-dependence in the Lyapunov exponent of a Boolean chaotic map
• Large-scale spatio-temporal patterns in a ring of non-locally coupled oscillators with a repulsive coupling
• Topological defects in spiral wave chimera states