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

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 100 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.

Chimera patterns in two-dimensional networks of coupled neurons

“…First found in identical and symmetrically coupled phase oscillators [2], chimera states have been the focus of extensive research for over a decade now. Both theoretical and experimental works have shown that this counter-intuitive collective phenomenon may arise in numerous systems including mechanical, chemical, electro-chemical, electrooptical, electronic, and superconducting coupled oscillators [3][4][5][6][7][8][9][10][11][12][13][14].…”

Chimera states in population dynamics: Networks with fragmented and hierarchical connectivities

“…Typical models that have been numerically investigated include the Kuramoto phase oscillator [7][8][9], periodic and chaotic maps [10,11], the Stuart-Landau model [13,14], the Van der Pol oscillator [12] as well as models addressing neuron dynamics such the FitzHughNagumo oscillator [15], the Hindmarsh-Rose model [16], the so-called SNIPER model of excitability type-I [17], or the Hodgkin-Huxley model [18]. Moreover, chimera states have been reported in populations of coupled pendula [19], in autonomous Boolean networks [20], in one-Following the theoretical predictions, chimera states were experimentally verified for the first time in populations of coupled chemical oscillators [23] and in optical coupled-map lattices realized by liquid-crystal light modulators [24]. Recently, in a purely mechanical experiment involving two groups of identical metronomes, it was shown that chimeras emerge naturally as a coexistence of two competing synchronization patterns [25].…”

Coherence-Resonance Chimeras in a Network of Excitable Elements

“…Originally discovered in a network of phase oscillators with a simple symmetric non-local coupling scheme [1,2], this sparked a tremendous activity of theoretical investigations . The first experimental evidence on chimera states was presented only one decade after their theoretical discovery [28][29][30][31][32][33][34][35][36][37][38]. In realworld systems chimera states might play a role, e.g., in power grids [39], in social systems [40], in the unihemispheric sleep of birds and dolphins [41], or in epileptic seizures [42].…”