scholarly journals Using noise to augment synchronization among oscillators

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jaykumar Vaidya ◽  
Mohammad Khairul Bashar ◽  
Nikhil Shukla
Keyword(s):  
White Noise ◽  
Coupling Strength ◽  
Coupled System ◽  
External Noise ◽  
Capacitive Coupling ◽  
Frequency Locking ◽  
Relaxation Oscillators ◽  
Computing Platforms ◽  
Analog Systems ◽  
Computational Properties

AbstractNoise is expected to play an important role in the dynamics of analog systems such as coupled oscillators which have recently been explored as a hardware platform for application in computing. In this work, we experimentally investigate the effect of noise on the synchronization of relaxation oscillators and their computational properties. Specifically, in contrast to its typically expected adverse effect, we first demonstrate that a common white noise input induces frequency locking among uncoupled oscillators. Experiments show that the minimum noise voltage required to induce frequency locking increases linearly with the amplitude of the oscillator output whereas it decreases with increasing number of oscillators. Further, our work reveals that in a coupled system of oscillators—relevant to solving computational problems such as graph coloring, the injection of white noise helps reduce the minimum required capacitive coupling strength. With the injection of noise, the coupled system demonstrates frequency locking along with the desired phase-based computational properties at 5 × lower coupling strength than that required when no external noise is introduced. Consequently, this can reduce the footprint of the coupling element and the corresponding area-intensive coupling architecture. Our work shows that noise can be utilized as an effective knob to optimize the implementation of coupled oscillator-based computing platforms.

GENERALIZED SYNCHRONIZATION, FREQUENCY-LOCKING AND PHASE-LOCKING OF COUPLED SINE CIRCLE MAPS

2001 ◽  
Vol 11 (08) ◽  
pp. 2245-2253
Author(s):  
WEN-XIN QIN
Keyword(s):  
Dynamical Systems ◽  
Invariant Manifold ◽  
Coupling Strength ◽  
Phase Locking ◽  
Coupled System ◽  
Generalized Synchronization ◽  
Frequency Locking ◽  
Local Systems ◽  
Circle Maps ◽  
The Individual

Applying invariant manifold theorem, we study the existence of generalized synchronization of a coupled system, with local systems being different sine circle maps. We specify a range of parameters for which the coupled system achieves generalized synchronization. We also investigate the relation between generalized synchronization, predictability and equivalence of dynamical systems. If the parameters are restricted in the specified range, then all the subsystems are topologically equivalent, and each subsystem is predictable from any other subsystem. Moreover, these subsystems are frequency locked even if the frequencies are greatly different in the absence of coupling. If the local systems are identical without coupling, then the widths of the phase-locked intervals of the coupled system are the same as those of the individual map and are independent of the coupling strength.

Phase Selective Oscillations in Two Noise Driven Synaptically Coupled Spiking Neurons

2015 ◽  
Vol 25 (07) ◽  
pp. 1540005
Author(s):  
Ilya Prokin ◽  
Ivan Tyukin ◽  
Victor Kazantsev
Keyword(s):  
Numerical Simulations ◽  
Coupled System ◽  
External Noise ◽  
Noise Signal ◽  
Feedback Mechanism ◽  
Spike Timing ◽  
Spiking Neurons ◽  
Time Lags ◽  
Tuning Parameters ◽  
Synaptic Inputs

The work investigates the influence of spike-timing dependent plasticity (STDP) mechanisms on the dynamics of two synaptically coupled neurons driven by additive external noise. In this setting, the noise signal models synaptic inputs that the pair receives from other neurons in a larger network. We show that in the absence of STDP feedbacks the pair of neurons exhibit oscillations and intermittent synchronization. When the synapse connecting the neurons is supplied with a phase selective feedback mechanism simulating STDP, induced dynamics of spikes in the coupled system resembles a phase locked mode with time lags between spikes oscillating about a specific value. This value, as we show by extensive numerical simulations, can be set arbitrary within a broad interval by tuning parameters of the STDP feedback.

scholarly journals Galvanic Phase Coupling of Superconducting Flux Qubits

2021 ◽  
Vol 11 (23) ◽  
pp. 11309
Author(s):  
Mun Dae Kim
Keyword(s):  
Coupling Strength ◽  
Fault Tolerant ◽  
Coupled System ◽  
Inductive Coupling ◽  
Galvanic Coupling ◽  
Flux Qubits ◽  
Superconducting Flux Qubits ◽  
Qubit Gate ◽  
Central Loop ◽  
Fundamental Boundary

We investigate the galvanic coupling schemes of superconducting flux qubits. From the fundamental boundary conditions, we obtain the effective potential of the coupled system of two or three flux qubits to provide the exact Lagrangian of the system. While usually the two-qubit gate has been investigated approximately, in this study we derive the exact inductive coupling strength between two flux qubits coupled directly and coupled through a connecting central loop. We observe that the inductive coupling strength needs to be included exactly to satisfy the criteria of fault-tolerant quantum computing.

scholarly journals Online Transcranial Random Noise stimulation improves perception at high levels of visual white noise

2020 ◽  
Author(s):  
Michael D. Melnick ◽  
Woon Ju Park ◽  
Sholei Croom ◽  
Shuyi Chen ◽  
Lorella Batelli ◽  
...  
Keyword(s):  
White Noise ◽  
Task Performance ◽  
Visual Processing ◽  
Random Noise ◽  
External Noise ◽  
Orientation Discrimination ◽  
Perceptual Training ◽  
Transcranial Random Noise Stimulation ◽  
Perceptual Performance ◽  
Underlying Mechanisms

AbstractTranscranial random noise stimulation (tRNS), a relatively recent addition to the field of non-invasive, electrical brain stimulation, has been shown to improve perceptual and cognitive functions across a wide variety of tasks. However, the underlying mechanisms of visual improvements caused by tRNS remain unclear. To study this question, we employed a well-established, equivalent-noise approach, which measures perceptual performance at various levels of external noise and is formalized by the Perceptual Template Model (PTM). This approach has been used extensively to infer the underlying mechanisms behind changes in visual processing, including those from perceptual training, adaptation and attention. Here, we used tRNS during an orientation discrimination task in the presence of increasing quantities of external visual white noise and fit the PTM to gain insights into the effects of tRNS on visual processing. Our results show that tRNS improves visual processing when stimulation is applied during task performance, but only at high levels of external visual white noise—a signature of improved external noise filtering. There were no significant effects of tRNS on task performance after the stimulation period. Of interest, the reported effects of tRNS on visual processing mimic those previously reported for endogenous spatial attention, offering a potential area of investigation for future work.

A Novel Dual-Mass Accelerometer Exploiting Mode Localization in Electrostatically Coupled Resonators

2021 ◽  
Author(s):  
Ming Lyu ◽  
Jian Zhao ◽  
Najib Kacem ◽  
Pengbo Liu
Keyword(s):  
Coupling Strength ◽  
Axial Load ◽  
Amplitude Ratio ◽  
Coupled System ◽  
Inertial Forces ◽  
Governing Equations ◽  
Coupled Resonators ◽  
Critical Amplitude ◽  
Mode Localization ◽  
Vibration Magnitude

Abstract A novel dual-mass accelerometer is proposed while exploiting the phenomenon of mode localization in two electrostatically coupled resonators with an adjustable coupling strength. The external inertial forces are transmitted differentially to the resonators in term of axial load change through the two levering mechanisms, breaking the balanced state and resulting in a drastic change in the amplitudes of the two resonators. Based on the Euler Bernoulli theory, the governing equations of the coupled system are derived and numerically solved. The sensitivity in term of relative shift of amplitude ratio can be improved by 4 orders of magnitude compared to frequency shift. Finally, the effect of the quality factor on the sensor dynamics has also been investigated, and the results show that it only affects the vibration magnitude of the resonators while operating below the critical amplitude.

The synchronization of asymmetric-structured electric coupling neuronal system

2018 ◽  
Vol 32 (04) ◽  
pp. 1850040 ◽  
Author(s):  
Guanping Wang ◽  
Wuyin Jin ◽  
Hao Liu ◽  
Wei Sun
Keyword(s):  
Time Delay ◽  
Coupling Strength ◽  
Single Neuron ◽  
Specific Area ◽  
Coupled System ◽  
Neuronal System ◽  
Electric Coupling ◽  
System Synchronization ◽  
Hr Model ◽  
Delay Difference

Based on the Hindmarsh–Rose (HR) model, the synchronization dynamics of asymmetric-structured electric coupling two neuronal system is investigated in this paper. It is discovered that when the time-delay scope and coupling strength for the synchronization are correlated positively under unequal time delay, the time-delay difference does not make a clear distinction between the two individual inter-spike intervals (ISI) bifurcation diagrams of the two coupled neurons. Therefore, the superficial difference of the system synchronization dynamics is not obvious for the unequal time-delay feedback. In the asymmetrical current incentives under asymmetric electric coupled system, the two neurons can only be almost completely synchronized in specific area of the interval which end-pointed with two discharge modes for a single neuron under different stimuli currents before coupling, but the intervention of time-delay feedback, together with the change of the coupling strength, can make the coupled system not only almost completely synchronized within anywhere in the front area, but also outside of it.

scholarly journals Time-delayed feedback in neurosystems

2009 ◽  
Vol 367 (1891) ◽  
pp. 1079-1096 ◽  
Author(s):  
Eckehard Schöll ◽  
Gerald Hiller ◽  
Philipp Hövel ◽  
Markus A Dahlem
Keyword(s):  
Time Delay ◽  
White Noise ◽  
Coupling Strength ◽  
Delay Time ◽  
Feedback Loop ◽  
Time Synchronization ◽  
Delayed Feedback ◽  
Amplitude Death ◽  
Large Delay ◽  
Time Delayed Feedback

The influence of time delay in systems of two coupled excitable neurons is studied in the framework of the FitzHugh–Nagumo model. A time delay can occur in the coupling between neurons or in a self-feedback loop. The stochastic synchronization of instantaneously coupled neurons under the influence of white noise can be deliberately controlled by local time-delayed feedback. By appropriate choice of the delay time, synchronization can be either enhanced or suppressed. In delay-coupled neurons, antiphase oscillations can be induced for sufficiently large delay and coupling strength. The additional application of time-delayed self-feedback leads to complex scenarios of synchronized in-phase or antiphase oscillations, bursting patterns or amplitude death.

scholarly journals Residual Predictive Information Flow in the Tight Coupling Limit: Analytic Insights from a Minimalistic Model

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 1010
Author(s):  
Benjamin Wahl ◽  
Ulrike Feudel ◽  
Jaroslav Hlinka ◽  
Matthias Wächter ◽  
Joachim Peinke ◽  
...  
Keyword(s):  
Information Flow ◽  
Coupling Strength ◽  
Social Groups ◽  
Coupled System ◽  
Model Description ◽  
Causal Connection ◽  
Noise Strength ◽  
Tight Coupling ◽  
Predictive Information ◽  
Analytic Expressions

In a coupled system, predictive information flows from the causing to the caused variable. The amount of transferred predictive information can be quantified through the use of transfer entropy or, for Gaussian variables, equivalently via Granger causality. It is natural to expect and has been repeatedly observed that a tight coupling does not permit to reconstruct a causal connection between causing and caused variables. Here, we show that for a model of interacting social groups, carried from the master equation to the Fokker–Planck level, a residual predictive information flow can remain for a pair of uni-directionally coupled variables even in the limit of infinite coupling strength. We trace this phenomenon back to the question of how the synchronizing force and the noise strength scale with the coupling strength. A simplified model description allows us to derive analytic expressions that fully elucidate the interplay between deterministic and stochastic model parts.

scholarly journals Numerical simulations of stochastic conformable space–time fractional Korteweg-de Vries and Benjamin–Bona–Mahony equations

2021 ◽  
Vol 10 (1) ◽  
pp. 77-90
Author(s):  
Leila Pedram ◽  
Davoud Rostamy
Keyword(s):  
White Noise ◽  
Numerical Simulations ◽  
External Noise ◽  
Space Time ◽  
Numerical Results ◽  
Time And Space ◽  
Modified Kudryashov Method ◽  
Kudryashov Method ◽  
De Vries

Abstract In this paper, we investigate the effect of white noise on conformable time and space fractional KdV and BBM equations. For this purpose, we convert these equations with external noise to homogeneous conformable time and space fractional KdV and BBM equations with defined transformation and then we solve them by modified Kudryashov method. We bring our numerical results in some figures in the last section.

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