Extreme events in a network of heterogeneous Josephson junctions

Abstract

We report rare and recurrent large spiking events in a heterogeneous network of superconducting Josephson junctions (JJ) connected through a resistive load and driven by a radio-frequency (rf) current in addition to a constant bias. The intermittent large spiking events show characteristic features of extreme events (EE) since they are larger than a statistically defined significant height. Under the influence of repulsive interactions and an impact of heterogeneity of damping parameters, the network splits into three sub-groups of junctions, one in incoherent rotational, another in coherent librational motion and a third sub-group originating EE. We are able to scan the whole population of junctions with their distinctive individual dynamical features either in EE mode or non-EE mode in parameter space. EE migrates spatially from one to another sub-group of junctions depending upon the repulsive strength and the damping parameter. For a weak repulsive coupling, all the junctions originate frequent large spiking events, in rotational motion when the average inter-spike-interval (ISI) is small, but it increases exponentially with repulsive interaction; it largely deviates from its exponential growth at a break point where EE triggers in a sub-group of junctions. The probability density of inter-event-intervals (IEI) in the subgroup exhibits a Poisson distribution. EE originates via bubbling instability of in-phase synchronization.

Emergence and mitigation of extreme events in a parametrically driven system with velocity-dependent potential

“…Hence, the suppressing nature of the external force, particularly in system (4), can be clearly seen in Fig. (14).…”

“…[12][13][14][15]. As far as the dynamical systems are concerned, these events occur in FitzHugh-Nagumo oscillators, Hindmarsh-Rose model, climatic models, Linéard system, memristor-based Linénard system, micromechanical system, electronic circuits, coupled Ikeda map, network of moving agents, network of Josephson junctions, dispersive wave models, Ginzburg-Landau model and nonlinear Schrödinger equation [4,5,8,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Further, in real-time engineering applications, these events are found in laser systems, plasma, optical fibers, and superfluid helium [6,7,28,29].…”

“…As far as coupled systems are concerned, extreme events are found to occur by a variety of mechanisms such as the breakdown of quasiperiodicity, instability in the antiphase synchronization [22], the opening of channel like structure [16], and the prototype events acting as precursors [5]. Besides, they also occur as a result of switching between the librational motion to rotational motion, the switching between precrisis to post-crisis region [14], and at the riddled basin, particularly in the region where both pure and mixed states are present [18]. In addition to the above, transient instabilities [32], attractor bubbling [33] and the influence of noise in multistable systems [34] are also some of the mechanisms behind the emergence of extreme events.…”

Predicting bursting in a complete graph of mixed population through reservoir computing

“…In presence of a periodic forcing or a shunted inductor, the RCSJ may reveal typical spiking and bursting behaviors [27,36,37,40]. An array of forced RCSJs may also reveal complex collective behavior (chimera, clustering, and extreme events) [41,42] under a global mean field interaction. As suggested above, we consider here a mixed population of RCSJs (total number of junctions is N d ), where p number of oscillators are in self-oscillatory mode and the rest of (N d − p) oscillators are in a quiescent state [26].…”

Chaos in fractional system with extreme events

“…Extreme events and spatiotemporal chaos were measured in a microcavity laser [ 22 ]. In the recent work [ 23 ], authors proposed a networks of Josephson junctions and obtained extreme events in a sub-population. Dynamical and statistical characteristics were studied indicating routes to extreme events [ 24 ].…”