UPPER BOUND OF THE TIME DERIVATIVE OF ENTROPY FOR A DYNAMICAL SYSTEM DRIVEN BY TWO KINDS OF COLORED NOISE

2009 ◽  
Vol 23 (02) ◽  
pp. 199-207 ◽  
Author(s):  
CAN-JUN WANG ◽  
DONG-CHENG MEI
Keyword(s):  
Dynamical System ◽  
Upper Bound ◽  
Correlation Time ◽  
Noise Intensity ◽  
Cross Correlation ◽  
Colored Noise ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Time Derivative ◽  
The Cross

The upper bound UB(t) of the time derivative of entropy for a dynamical system driven by both additive colored noise and multiplicative colored noise with colored cross-correlation is investigated. Based on the Fokker–Planck equation, the effects of the parameters on UB(t) are analyzed. The results show that: (i) α (the multiplicative noise intensity), D (the additive noise intensity) and τ2 (the correlation time of the additive noise) always enhance UB (t) monotonically; (ii) λ (the intensity of the cross-correlation between the multiplicative noise and the additive noise), τ1 (the correlation time of the multiplicative noise), τ3 (the correlation time of the cross-correlation) and γ (the dissipative constant) all possess a minimum, i.e., UB (t) decreases for small values and increases for large values.

Colored correlated multiplicative and additive Gaussian colored noises-induced transition of a piecewise nonlinear bistable model

2017 ◽  
Vol 31 (28) ◽  
pp. 1750256 ◽  
Author(s):  
Yong-Feng Guo ◽  
Ya-Jun Shen ◽  
Bei Xi ◽  
Jian-Guo Tan
Keyword(s):  
Steady State ◽  
Correlation Time ◽  
Noise Intensity ◽  
Cross Correlation ◽  
Colored Noise ◽  
Nonlinear Phenomena ◽  
Steady State Probability ◽  
Model Driven ◽  
Correlation Strength ◽  
The Cross

In this paper, we investigate the steady-state properties of a piecewise nonlinear bistable model driven by multiplicative and additive Gaussian colored noises with colored cross-correlation. Using the unified colored noise approximation, we derive the analytical expression of the steady-state probability density (SPD) function. Then the effects of colored correlated Gaussian colored noises on SPD are presented. According to the research results, it is found that there appear some new nonlinear phenomena in this system. The multiplicative colored noise intensity, the additive colored noise intensity and the cross-correlation strength between noises can induce the transition. However, the transition cannot be induced by the auto-correlation time of multiplicative and additive Gaussian colored noises as well as the cross-correlation time between noises.

Nonequilibrium Phenomena in Globally Coupled Phase Oscillators: Noise-Induced Bifurcations, Clustering, and Switching

1997 ◽  
Vol 07 (04) ◽  
pp. 917-922
Author(s):  
Seon Hee Park ◽  
Seunghwan Kim ◽  
Seung Kee Han
Keyword(s):  
Phase Transition ◽  
Noise Intensity ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Critical Value ◽  
Phase Oscillators ◽  
Deterministic Systems ◽  
Nonequilibrium Phenomena ◽  
Noise Models ◽  
Coupled Phase Oscillators

The Nonequilibrium phenomena in a class of globally coupled phase oscillators systems with multiplicative noise are studied. It is shown that at the critical value of the noise intensity the systems undergo a phase transition and converge to clustered states. We also show that the time delay in the interaction between oscillators gives rise to the switching phenomena of clusters. These phenomena are noise-induced effects which cannot be seen in the deterministic systems or in the simple additive noise models.

scholarly journals Stochastic Resonance in Neuronal Network Motifs with Ornstein-Uhlenbeck Colored Noise

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xuyang Lou
Keyword(s):  
Stochastic Resonance ◽  
Correlation Time ◽  
Noise Intensity ◽  
Colored Noise ◽  
Stochastic Dynamics ◽  
Signal To Noise Ratio ◽  
Network Motif ◽  
Control Parameters ◽  
Noise Process ◽  
Chemical Coupling

We consider here the effect of the Ornstein-Uhlenbeck colored noise on the stochastic resonance of the feed-forward-loop (FFL) network motif. The FFL motif is modeled through the FitzHugh-Nagumo neuron model as well as the chemical coupling. Our results show that the noise intensity and the correlation time of the noise process serve as the control parameters, which have great impacts on the stochastic dynamics of the FFL motif. We find that, with a proper choice of noise intensities and the correlation time of the noise process, the signal-to-noise ratio (SNR) can display more than one peak.

The New Method for Power Quality Indices Estimation

2014 ◽  
Vol 1006-1007 ◽  
pp. 1066-1070
Author(s):  
Ying Hai ◽  
Jing Yu Chen
Keyword(s):  
Computer Simulation ◽  
Power Quality ◽  
Computational Efficiency ◽  
Correlation Matrix ◽  
Cross Correlation ◽  
Additive Noise ◽  
Rotational Invariance ◽  
New Method ◽  
Quality Indices ◽  
The Cross

In this paper, the rotational invariance technique (ESPRIT) based on the cross-correlation matrix is used to estimate the power quality indices (PQI) . This method enables the alleviation of the effects of additive noise, and improves the computational efficiency. Computer simulation and experimental were performed on synthesized signals to assess the performance of the method.

scholarly journals NONMONOTONIC PATTERN FORMATION IN THREE SPECIES LOTKA–VOLTERRA SYSTEM WITH COLORED NOISE

2005 ◽  
Vol 05 (02) ◽  
pp. L305-L311 ◽  
Author(s):  
A. FIASCONARO ◽  
D. VALENTI ◽  
B. SPAGNOLO
Keyword(s):  
Pattern Formation ◽  
Noise Intensity ◽  
Colored Noise ◽  
Multiplicative Noise ◽  
Volterra Equations ◽  
Volterra System ◽  
Spatiotemporal Evolution ◽  
Species Concentration ◽  
Interacting Species ◽  
Nonmonotonic Behavior

A coupled map lattice of generalized Lotka–Volterra equations in the presence of colored multiplicative noise is used to analyze the spatiotemporal evolution of three interacting species: one predator and two preys symmetrically competing each other. The correlation of the species concentration over the grid as a function of time and of the noise intensity is investigated. The presence of noise induces pattern formation, whose dimensions show a nonmonotonic behavior as a function of the noise intensity. The colored noise induces a greater dimension of the patterns with respect to the white noise case and a shift of the maximum of its area towards higher values of the noise intensity.

Hydraulic Actuator Internal Leakage Detection Using Cross-Correlation Time Series Analysis

2014 ◽  
Author(s):  
Morgan May ◽  
Nariman Sepehri ◽  
Witold Kinsner
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Correlation Time ◽  
Cross Correlation ◽  
Dynamic Performance ◽  
Cylinder Wall ◽  
Hydraulic Actuator ◽  
Series Analysis ◽  
Piston Seal ◽  
The Cross

As a hydraulic actuator is used over time, the piston seal that closes the gap between the moveable piston and the cylinder wall wears. This results in the fluid to eventually being able to flow across the piston and between the cylinder chambers. Although no fluid is lost from the circuit, the dynamic performance of the system is affected since only a portion of the flow delivered to the actuator is available to move the piston against the load. Leakage across the piston introduces a flow deadband, which can lead to servoing errors. This paper presents an approach based on the cross-correlation time-series analysis to determine the health of hydraulic actuator internal seals. Pressure signals obtained directly from routine operations are analyzed using the cross-correlation function. The method presented in this paper is shown to be capable of detecting leakages as small as 0.069 l/min.

Upper Bound on the Cross-Correlation between Two Decimated Sequences

2017 ◽  
Vol E100.B (5) ◽  
pp. 837-842
Author(s):  
Chang-Min CHO ◽  
Wijik LEE ◽  
Jong-Seon NO ◽  
Young-Sik KIM
Keyword(s):  
Upper Bound ◽  
Cross Correlation ◽  
The Cross
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