Effects of Time Delay on the Bistable System Subjected to Correlated Noises

2007 ◽  
Vol 24 (11) ◽  
pp. 3074-3076 ◽  
Author(s):  
Nie Lin-Ru ◽  
Mei Dong-Cheng
Keyword(s):  
Time Delay ◽  
Bistable System ◽  
Correlated Noises

SIMULATION STUDY OF NOISE-ENHANCED STABILITY AND RESONANT ACTIVATION IN A BISTABLE SYSTEM INDUCED BY TIME DELAY

2011 ◽  
Vol 25 (02) ◽  
pp. 141-149 ◽  
Author(s):  
CHUN LI ◽  
LUCHUN DU ◽  
DONGCHENG MEI
Keyword(s):  
Time Delay ◽  
Thermal Activation ◽  
Multiplicative Noise ◽  
Bistable System ◽  
Peak Structure ◽  
Activation Rate ◽  
Linear Delay ◽  
Resonant Activation ◽  
Correlated Noises ◽  
Enhanced Stability

The thermal activation problem of a bistable system driven by correlated noises with time delay is investigated by means of numerical simulations. The simulation results indicate: (1) For the case of the bistable system with linear delay, the phenomenon of noise enhanced stability (NES) is enforced by increasing delay time τ as the multiplicative noise intensity D is smaller, but is weakened as D is larger. (2) For the case of the bistable system with cubic delay, the NES becomes faintness as τ increases. (3) For the case of the bistable system with global delay, the NES is still restrained by increasing τ with smaller D, and in some circumstances, the activation rate as a function of τ exists a peak structure, which demonstrating the emergence of resonant activation.

Effects of time delay on the statistical fluctuations for a bistable system driven by cross-correlated noises

Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
Chun-hua Zeng ◽  
Xiao-feng Zhou ◽  
Shu-fen Tao
Keyword(s):  
Time Delay ◽  
Delay Time ◽  
Operator Method ◽  
Dynamical Variable ◽  
Small Time ◽  
Bistable System ◽  
Statistical Fluctuations ◽  
Small Time Delay ◽  
Projection Operator Method ◽  
Correlated Noises

AbstractWe study the effects of time delay on the normalized correlation function C(s) and the associated relaxation time T c for a bistable system with correlations between multiplicative and additive white noises under the condition of small time delay. Using the projection operator method, the expressions of T c and C(s) are obtained. Based on numerical computations, it is found that the delay time τ slows down the rate of fluctuation decay of dynamical variable for the presence of positive feedback intensity (∈ > 0), while speeds up the rate of fluctuation decay of dynamical variable for the presence of negative feedback intensity (∈ < 0). The effects of the delay time τ on the T c and C(s) are entirely opposite for ∈ 〉 0 and ∈ < 0.

scholarly journals Optimal Linear Estimators for Time-Delay Systems with Fading Measurements and Correlated Noises

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Yazhou Li ◽  
Jiayi Li ◽  
Xin Wang
Keyword(s):  
Time Delay ◽  
Minimum Variance ◽  
Delay Systems ◽  
Multiplicative Noises ◽  
Linear Estimators ◽  
Discrete Linear Systems ◽  
Estimation Problems ◽  
Optimal Linear ◽  
State Augmentation ◽  
Correlated Noises

The optimal linear estimation problems are investigated in this paper for a class of discrete linear systems with fading measurements and correlated noises. Firstly, the fading measurements occur in a random way where the fading probabilities are regulated by probability mass functions in a given interval. Furthermore, time-delay exists in the system state and observation simultaneously. Additionally, the multiplicative noises are considered to describe the uncertainty of the state. Based on the projection theory, the linear minimum variance optimal linear estimators, including filter, predictor, and smoother are presented in the paper. Compared with conventional state augmentation, the new algorithm is finite-dimensionally computable and does not increase computational and storage load when the delay is large. A numerical example is provided to illustrate the effectiveness of the proposed algorithms.

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