Stochastic Generation and Deformation of Toroidal Oscillations in Neuron Model

2018 ◽  
Vol 28 (06) ◽  
pp. 1850070 ◽  
Author(s):  
Irina Bashkirtseva ◽  
Lev Ryashko ◽  
Evdokia Slepukhina
Keyword(s):  
Neuron Model ◽  
Confidence Regions ◽  
Time Interval ◽  
Dynamical Structure ◽  
Deterministic System ◽  
Phase Duration ◽  
Stochastic Generation ◽  
Stochastic Sensitivity ◽  
Power Spectral ◽  
Deterministic Trajectories

The stochastic Hindmarsh–Rose neuron model in the parametric regions of complex nonlinear dynamics with quiescent and torus bursting regimes is studied. We show that in the zone where the deterministic system exhibits the quiescence, noise can lead to the generation of toroidal dynamical structure with the transition to the bursting regime. The studies of dispersion of random trajectories as well as power spectral density and interspike intervals distribution confirm these changes in system dynamics. Moreover, the stochastic emergence of torus is followed by the noise-induced chaotization. We show that the generation of the torus bursting oscillations is associated with the specificity of the arrangement of deterministic trajectories in the vicinity of the equilibrium as well as its stochastic sensitivity. A probabilistic mechanism of the stochastic generation of torus is investigated on the basis of the analysis of the stochastic sensitivity and geometry of confidence regions. We also show that in the parametric range of the torus bursting, noise can lead to the increase of number of bursts per time interval and to the reduction of spiking and quiescent phase duration.

scholarly journals Improving the Stochastic Model of Ionospheric Delays for BDS Long-Range Real-Time Kinematic Positioning

2021 ◽  
Vol 13 (14) ◽  
pp. 2739
Author(s):  
Huizhong Zhu ◽  
Jun Li ◽  
Longjiang Tang ◽  
Maorong Ge ◽  
Aigong Xu
Keyword(s):  
Real Time ◽  
Long Range ◽  
Ionospheric Delay ◽  
Time Interval ◽  
Short Time Interval ◽  
Dual Frequency ◽  
Triple Frequency ◽  
Ambiguity Fixing ◽  
Power Spectral ◽  
Observation Noise

Although ionosphere-free (IF) combination is usually employed in long-range precise positioning, in order to employ the knowledge of the spatiotemporal ionospheric delays variations and avoid the difficulty in choosing the IF combinations in case of triple-frequency data processing, using uncombined observations with proper ionospheric constraints is more beneficial. Yet, determining the appropriate power spectral density (PSD) of ionospheric delays is one of the most important issues in the uncombined processing, as the empirical methods cannot consider the actual ionosphere activities. The ionospheric delays derived from actual dual-frequency phase observations contain not only the real-time ionospheric delays variations, but also the observation noise which could be much larger than ionospheric delays changes over a very short time interval, so that the statistics of the ionospheric delays cannot be retrieved properly. Fortunately, the ionospheric delays variations and the observation noise behave in different ways, i.e., can be represented by random-walk and white noise process, respectively, so that they can be separated statistically. In this paper, we proposed an approach to determine the PSD of ionospheric delays for each satellite in real-time by denoising the ionospheric delay observations. Based on the relationship between the PSD, observation noise and the ionospheric observations, several aspects impacting the PSD calculation are investigated numerically and the optimal values are suggested. The proposed approach with the suggested optimal parameters is applied to the processing of three long-range baselines of 103 km, 175 km and 200 km with triple-frequency BDS data in both static and kinematic mode. The improvement in the first ambiguity fixing time (FAFT), the positioning accuracy and the estimated ionospheric delays are analysed and compared with that using empirical PSD. The results show that the FAFT can be shortened by at least 8% compared with using a unique empirical PSD for all satellites although it is even fine-tuned according to the actual observations and improved by 34% compared with that using PSD derived from ionospheric delay observations without denoising. Finally, the positioning performance of BDS three-frequency observations shows that the averaged FAFT is 226 s and 270 s, and the positioning accuracies after ambiguity fixing are 1 cm, 1 cm and 3 cm in the East, North and Up directions for static and 3 cm, 3 cm and 6 cm for kinematic mode, respectively.

scholarly journals CONTROLLING STOCHASTIC OSCILLATIONS CLOSE TO A HOPF BIFURCATION BY TIME-DELAYED FEEDBACK

2005 ◽  
Vol 05 (02) ◽  
pp. 281-295 ◽  
Author(s):  
E. SCHÖLL ◽  
A. G. BALANOV ◽  
N. B. JANSON ◽  
A. NEIMAN
Keyword(s):  
Hopf Bifurcation ◽  
Delayed Feedback ◽  
Van Der Pol Oscillator ◽  
Deterministic System ◽  
Control Force ◽  
Stochastic Delay ◽  
Power Spectral ◽  
Delay Differential ◽  
Stochastic Oscillations ◽  
Time Delayed Feedback

We study the effect of a time-delayed feedback upon a Van der Pol oscillator under the influence of white noise in the regime below the Hopf bifurcation where the deterministic system has a stable fixed point. We show that both the coherence and the frequency of the noise-induced oscillations can be controlled by varying the delay time and the strength of the control force. Approximate analytical expressions for the power spectral density and the coherence properties of the stochastic delay differential equation are developed, and are in good agreement with our numerical simulations. Our analytical results elucidate how the correlation time of the controlled stochastic oscillations can be maximized as a function of delay and feedback strength.

Rolling Bearing Safety Region Estimation Based on Information Entropy

2014 ◽  
Vol 614 ◽  
pp. 40-43
Author(s):  
Hao Jun Sun ◽  
Lei Zhang ◽  
Yong Qin
Keyword(s):  
Roller Bearing ◽  
Rolling Bearing ◽  
Singular Value ◽  
Time Interval ◽  
Spectral Entropy ◽  
Vibration Acceleration ◽  
State Identification ◽  
Power Spectral ◽  
Acceleration Data ◽  
Bearing Condition Monitoring

The basic idea of safety region is introduced into roller bearing condition monitoring. Power Spectral Entropy, Singular value Entropy are used comprehensively for the estimation of the safety region and the identification of normal state and faulty state for the roller bearing operational status. First, the vibration acceleration data was segmented according to a certain time interval and then establish Power Spectral Entropy, Singular value Entropy as characteristics of roller bearings. Finally, SVM was used for the estimation of the safety region of the roller bearing operation state, and multi-class SVM was used of the identification of the four states. The results show that both the safety region estimation and state identification are accurate, and confirm the validity of the method.

Finite-time higher-order moment state estimation for Markov jump linear system with time-correlated measurement noise

2021 ◽  
pp. 014233122199012
Author(s):  
Ziheng Zhou ◽  
Xiaoli Luan ◽  
Fei Liu
Keyword(s):  
State Estimation ◽  
Discrete Time ◽  
Finite Time ◽  
Higher Order ◽  
Measurement Noise ◽  
Order Moment ◽  
Time Interval ◽  
Deterministic System ◽  
Markov Jump ◽  
Moment State

In the present study, a higher-order moment state estimation problem in a finite time interval for the discrete-time Markov jump linear systems (MJLS) is investigated. Moreover, time-correlated noise in measurements is considered. Initially, the measruement differencing approach is applied to convert the time-correlated measurement noise to an uncorrelated noise. Then the cumulant generating function is utilized to solve the stochastic jumping problem of MJLS, by which the discrete-time MJLS is transformed into a deterministic system. In this way, the transformed deterministic system has the same norm with a higher-order moment of the original state. Finally, a finite-time state estimation algorithm is proposed to guarantee that the higher-order moment of error trajectory remains within a pre-specified bound over a given time interval. In order to evaluate the performance of the proposed method, some test cases are applied. Obtained results prove the accuracy and efficiency of the proposed method.

Microtremor analysis of local geological conditions

1976 ◽  
Vol 66 (1) ◽  
pp. 45-60 ◽  
Author(s):  
Lewis J. Katz
Keyword(s):  
Transfer Functions ◽  
Response Spectra ◽  
Earthquake Risk ◽  
Time Interval ◽  
Time Intervals ◽  
Local Site ◽  
Power Spectral ◽  
Geological Conditions ◽  
Long Time ◽  
Positive Correlations

abstract The application of microtremor spectra in predicting frequency-dependent amplification effects of local site geology was investigated. Long time-interval (> 45 min) microtremor data were used to estimate Power Spectral Density (PSD) plots. Peaks occurring in these PSD plots were correlated with peaks of transfer functions (Haskell, 1960 and 1962) calculated from known geological models. The resulting apparent positive correlations indicate that a procedure of estimating PSD plots from long time intervals of microtremor data would be useful in predicting response spectra for earthquake risk evaluation.

Analysis of Spatially Extended Excitable Izhikevich Neuron Model near Instability

2021 ◽  
Author(s):  
Arnab Mondal ◽  
Argha Mondal ◽  
S. Sharma ◽  
Ranjit Kumar Upadhyay
Keyword(s):  
Neuron Model ◽  
Nearest Neighbor ◽  
Electrical Potential ◽  
Coupled Systems ◽  
Biophysical Model ◽  
Deterministic System ◽  
Amplitude Equations ◽  
Riccati Differential Equation ◽  
Analytical Scheme ◽  
Izhikevich Neuron Model

Abstract The article focuses on the issue of a spatiotemporal excitable biophysical model that describes the propagation of electrical potential called spikes to model the diffusion induced dynamics based on an analytical development of amplitude equations. Considering the Izhikevich neuron model consisting of coupled systems of ODEs , we demonstrate various results of spatiotemporal architecture ( PDEs ) using a suitable parameter regime. We analytically perform the saddle node bifurcation and Hopf bifurcation analysis with bifurcating periodic solutions that show the transition phases in the system dynamics. We study different types of firing patterns both analytically and numerically by the formation of Riccati differential equation. To examine the characteristics of diffusive instabilities, we use Turing amplitude equations by multiscaling method and then expansion in powers of a small control parameter. The instabilities and Turing bifurcation are established using the theoretical analysis and numerical simulations. The spatial system has potential effects on the deterministic system as a result of the diffusive matrices with various couplings and the coupled oscillators with this nearest neighbor coupling show synchronization measured by the synchronization factor analysis. Our results qualitatively reproduce different phenomena of the extended excitable system based with an efficient analytical scheme.

scholarly journals Stochastic sensitivity of quasiperiodic and chaotic attractors of the discrete Lotka-Volterra model

2020 ◽  
Vol 55 ◽  
pp. 19-32
Author(s):  
A.V. Belyaev ◽  
T.V. Perevalova
Keyword(s):  
Period Doubling ◽  
Basins Of Attraction ◽  
Invariant Curve ◽  
Volterra Model ◽  
Chaotic Attractors ◽  
Deterministic System ◽  
System A ◽  
Stochastic Sensitivity ◽  
Two Parameters ◽  
Random States

The aim of the study presented in this article is to analyze the possible dynamic modes of the deterministic and stochastic Lotka-Volterra model. Depending on the two parameters of the system, a map of regimes is constructed. Parametric areas of existence of stable equilibria, cycles, closed invariant curves, and also chaotic attractors are studied. The bifurcations such as the period doubling, Neimark-Sacker and the crisis are described. The complex shape of the basins of attraction of irregular attractors (closed invariant curve and chaos) is demonstrated. In addition to the deterministic system, the stochastic system, which describes the influence of external random influence, is discussed. Here, the key is to find the sensitivity of such complex attractors as a closed invariant curve and chaos. In the case of chaos, an algorithm to find critical lines giving the boundary of a chaotic attractor, is described. Based on the found function of stochastic sensitivity, confidence domains are constructed that allow us to describe the form of random states around a deterministic attractor.

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