The Effects of Time Delay on Stochastic Resonance in a Bistable System with Correlated Noises

2009 ◽  
Vol 137 (4) ◽  
pp. 625-638 ◽  
Author(s):  
Dong Cheng Mei ◽  
Lu Chun Du ◽  
Can Jun Wang
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Bistable System ◽  
Correlated Noises

Stochastic resonance in asymmetric time-delayed bistable system under multiplicative and additive noise and its applications in bearing fault detection

2019 ◽  
Vol 33 (28) ◽  
pp. 1950341 ◽  
Author(s):  
Lifang He ◽  
Dayun Hu ◽  
Gang Zhang ◽  
Siliang Lu
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Additive Noise ◽  
Random Force ◽  
Small Time ◽  
Delayed Feedback ◽  
Bistable System ◽  
Bearing Fault ◽  
Strength Formula ◽  
Time Delayed Feedback

The asymmetric bistable system with time delays in the feedback force and random force under multiplicative and additive Gaussian noise is studied. Using the small time delay approximation approach and time-delayed Fokker–Planck equations (FPE), the signal-to-noise ratio (SNR) of the proposed stochastic system is obtained. The stochastic resonance (SR) phenomena influenced by parameters — including system parameters [Formula: see text], [Formula: see text], asymmetry parameter [Formula: see text], time delay [Formula: see text], strength [Formula: see text] of the time-delayed feedback, noise intensities [Formula: see text] and [Formula: see text] of multiplicative and additive noise, and correlation strength [Formula: see text] between two noises, are also analyzed by numerical simulations. Results demonstrate that the SR performance of the asymmetric bistable system is superior to one symmetric bistable system. Besides, both time delay and strength of time-delayed feedback could enhance the SR to some extent. Then, the asymmetric time-delayed bistable SR (ATDBSR) method is used to the bearing fault diagnosis. The engineering applications of the ATDBSR method are realized and the value of the method is verified by effective experimental results.

STOCHASTIC RESONANCE IN A TIME-DELAYED BISTABLE SYSTEM WITH COLORED COUPLING BETWEEN NOISE TERMS

2012 ◽  
Vol 26 (30) ◽  
pp. 1250149 ◽  
Author(s):  
XIAOQIN LUO ◽  
DAN WU ◽  
SHIQUN ZHU
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Coupling Strength ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Bistable System ◽  
Initial Condition

The phenomenon of stochastic resonance (SR) in a time-delayed bistable system with colored coupling between multiplicative and additive noise terms is investigated. The SR can be induced by the multiplicative noise, the time delay and the coupling strength between noise terms. Meanwhile, the SR is affected by the initial condition of the system.

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.

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