Improving the precision of noisy oscillators
نویسنده
چکیده
We consider how the period of an oscillator is affected by white noise, with special attention given to the cases of additive noise and parameter fluctuations. Our treatment is based upon the concepts of isochrons, which extend the notion of the phase of a stable periodic orbit to the basin of attraction of the periodic orbit, and phase response curves, which can be used to understand the geometry of isochrons near the periodic orbit. This includes a derivation of the leading-order effect of noise on the statistics of an oscillator’s period. Several examples are considered in detail, which illustrate the use and validity of the theory, and demonstrate how to improve a noisy oscillator’s precision by appropriately tuning system parameters or operating away fromabifurcationpoint. It is also shown that appropriately timed impulsive kicks can give further improvements to oscillator precision. © 2014 Elsevier B.V. All rights reserved.
منابع مشابه
Minimizing Loss of Information at Competitive PLIP Algorithms for Image Segmentation with Noisy Back Ground
In this paper, two training systems for selecting PLIP parameters have been demonstrated. The first compares the MSE of a high precision result to that of a lower precision approximation in order to minimize loss of information. The second uses EMEE scores to maximize visual appeal and further reduce information loss. It was shown that, in the general case of basic addition, subtraction, or mul...
متن کاملImproving the frequency precision of oscillators by synchronization.
Improving the frequency precision by synchronizing a lattice of N oscillators with disparate frequencies is studied in the phase reduction limit. In the general case where the coupling is not purely dissipative the synchronized state consists of targetlike waves radiating from a local source, which is a region of higher-frequency oscillators. In this state the improvement of the frequency preci...
متن کاملPersistent Cell-Autonomous Circadian Oscillations in Fibroblasts Revealed by Six-Week Single-Cell Imaging of PER2::LUC Bioluminescence
Biological oscillators naturally exhibit stochastic fluctuations in period and amplitude due to the random nature of molecular reactions. Accurately measuring the precision of noisy oscillators and the heterogeneity in period and strength of rhythmicity across a population of cells requires single-cell recordings of sufficient length to fully represent the variability of oscillations. We found ...
متن کاملA method to solve the problem of missing data, outlier data and noisy data in order to improve the performance of human and information interaction
Abstract Purpose: Errors in data collection and failure to pay attention to data that are noisy in the collection process for any reason cause problems in data-based analysis and, as a result, wrong decision-making. Therefore, solving the problem of missing or noisy data before processing and analysis is of vital importance in analytical systems. The purpose of this paper is to provide a metho...
متن کاملPersistence, period and precision of autonomous cellular oscillators from the zebrafish segmentation clock
In vertebrate development, the sequential and rhythmic segmentation of the body axis is regulated by a "segmentation clock". This clock is comprised of a population of coordinated oscillating cells that together produce rhythmic gene expression patterns in the embryo. Whether individual cells autonomously maintain oscillations, or whether oscillations depend on signals from neighboring cells is...
متن کامل