Common White Noise Research Articles

Desynchronization of stochastically synchronized neural populations through phase distribution control: a numerical simulation approach

Stochastic synchrony, also known as noise-induced synchronization that leads to phase coherence, arises when a set of uncoupled neurons synchronizes to a common white noise input or other types of non-Gaussian noise. Evidence of abnormally high noise-induced synchronization, or impairment in synchronous activity, has been found in several pathologies such as epilepsy. Therefore, controlling the stochastic synchronization of neurons can have a significant effect on preventing seizures in epilepsy. The main aim of this study is to develop a fast and reliable numerical method to simulate controlling synchronization in a population of noisy and uncoupled neural oscillators. The control algorithm is based on phase reduction and uses the probability phase distribution partial differential equation to change the distribution of oscillators to the desired one. The accuracy and power consumption are two main issues that should be considered in the simulations. In this paper, a new numerical method called the generalized Lagrange Jacobi Gauss–Lobatto collocation method in space and backward-Euler scheme in time is applied to overcome the difficulties of the problem effectively. The resulting full-discrete scheme of the partial differential equation is a linear system of algebraic equations per time step which is solved via QR algorithm. Finally, the proposed algorithm is applied to various neural dynamical models with different phase response curves and investigates them in different factors such as computing time, energy consumption, and accuracy to confirm the applicability of the developed numerical method.

Using noise to augment synchronization among oscillators

Noise 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.

Synchronization of stochastic hybrid oscillators driven by a common switching environment.

Many systems in biology, physics, and chemistry can be modeled through ordinary differential equations (ODEs), which are piecewise smooth, but switch between different states according to a Markov jump process. In the fast switching limit, the dynamics converges to a deterministic ODE. In this paper, we suppose that this limit ODE supports a stable limit cycle. We demonstrate that a set of such oscillators can synchronize when they are uncoupled, but they share the same switching Markov jump process. The latter is taken to represent the effect of a common randomly switching environment. We determine the leading order of the Lyapunov coefficient governing the rate of decay of the phase difference in the fast switching limit. The analysis bears some similarities to the classical analysis of synchronization of stochastic oscillators subject to common white noise. However, the discrete nature of the Markov jump process raises some difficulties: in fact, we find that the Lyapunov coefficient from the quasi-steady-state approximation differs from the Lyapunov coefficient one obtains from a second order perturbation expansion in the waiting time between jumps. Finally, we demonstrate synchronization numerically in the radial isochron clock model and show that the latter Lyapunov exponent is more accurate.

Noise analysis of continuous GPS coordinate time series for CMONOC

The Crustal Movement Observation Network of China (CMONOC) is one of the major scientific infrastructures, mainly using Global Positioning System (GPS) measurements, to monitor crustal deformation in the Chinese mainland. In this paper, decade-long coordinate time series of 26 continuous GPS sites of CMONOC are analyzed for their noise content using maximum likelihood estimation (MLE). We study the noise properties of continuous GPS time series of CMONOC for the unfiltered, filtered solutions and also the common mode signals in terms of power law plus white noise model. In the spatial filtering, we remove for every time series a common mode error that was estimated from a modified stacking of position residuals from other sites within ∼1000km of the selected site. We find that the common mode signal in our network has a combination of spatially correlated flicker noise and a common white noise with large spatial extent. We demonstrate that for the unfiltered solutions of CMONOC continuous GPS sites the main colored noise is a flicker process, with a mean spectral index of ∼1. For the filtered solutions, the main colored noise is a general power law process, indicating that a major number of the filtered regional solutions have a combination of noise sources or local effects. The velocity uncertainties from CMONOC continuous GPS coordinate time series may be underestimated by factors of 8–16 if a pure white noise model is assumed. In addition, using a white plus flicker noise model, the median values of velocity errors for the unfiltered solutions are 0.16 (north), 0.17 (east) and 0.58 (vertical)mm/yr, and the median values for the filtered solutions are 0.09 (north), 0.10 (east) and 0.40 (vertical)mm/yr.

Nonautonomous noise-induced synchronization

Two uncoupled Van der Pol oscillators driven by a common external harmonic signal and common white noise have been considered as a sample system. It was shown that the length of the time interval preceding the synchronous mode arising is inversely proportional to the value of the noise intensity.

Invariance of Frequency Difference in Nonresonant Entrainment of Detuned Oscillators Induced by Common White Noise

We studied the entrainment of two uncoupled detuned limit cycle oscillators subjected to a common external white Gaussian noise. We found a novel type of entrainment behavior for a general class of oscillators: as noise intensity increases, the phases of the two oscillators come to be almost always locked with each other although there is no frequency locking in the sense that the mean frequency difference remains the same as the natural frequency difference. We also show that a common noise induces a macroscopic oscillation with no frequency locking in a population of detuned oscillators.

Synchronization of self-sustained oscillators by common white noise

We study the stability of self-sustained oscillations under the influence of external noise. For small-noise amplitude a phase approximation for the Langevin dynamics is valid. A stationary distribution of the phase is used for an analytic calculation of the maximal Lyapunov exponent. We demonstrate that for small noise the exponent is negative, which corresponds to synchronization of oscillators.

Spectral distance measures between continuous-time vector Gaussian processes (Corresp.)

A new expression for the Chernoff distance between two continuous-time stationary vector Gaussian processes that contain a common white noise component and have equal means is derived. The expression is given in terms of the spectral density matrices for large observation interval <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> . The expression is then used for deriving upper and lower bounds to the Bayes probability of error. Both bounds converge to zero exponentially in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> . It is also shown that the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</tex> -divergence and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</tex> -divergence can be easily evaluated in the frequency domain by differentiation of the Chernoff distance.