scholarly journals The reliability of logical operation in a one-dimensional bistable system induced by non-Gaussian noise

2013 ◽  
Vol 62 (19) ◽  
pp. 190510
Author(s):  
Jin Xiao-Qin ◽  
Xu Yong ◽  
Zhang Hui-Qing
Keyword(s):  
Gaussian Noise ◽  
Bistable System ◽  
Logical Operation ◽  
One Dimensional ◽  
Non Gaussian

Comparison of Bistable Systems and Matched Filters in Non-Gaussian Noise

2016 ◽  
Vol 15 (01) ◽  
pp. 1650003 ◽  
Author(s):  
Xinming Zhang ◽  
Jianfeng Yan ◽  
Fabing Duan
Keyword(s):  
Gaussian Noise ◽  
Matched Filter ◽  
Signal To Noise Ratio ◽  
Internal Noise ◽  
Bistable System ◽  
Lower Probability ◽  
Probability Of Error ◽  
Bistable Systems ◽  
Comparison Results ◽  
Non Gaussian

In this paper, we report that for a weak signal buried in the heavy-tailed noise, the bistable system can outperform the matched filter, yielding a higher output signal-to-noise ratio (SNR) or a lower probability of error. Moreover, by adding mutually independent internal noise components to an array of bistable systems, the output SNR or the probability of error can be further improved via the mechanism of stochastic resonance (SR). These comparison results demonstrate the potential capability of bistable systems for detecting weak signals in non-Gaussian noise environments.

The Balanced Dynamical Bridge: Detection and Sensitivity to Parameter Shifts and Non-Gaussian Noise

2012 ◽  
Author(s):  
Nicholas J. Miller ◽  
Pavel M. Polunin ◽  
Mark I. Dykman ◽  
Steven W. Shaw
Keyword(s):  
Gaussian Noise ◽  
Bistable System ◽  
Measurement Time ◽  
Nano Scale ◽  
Shot Noise Process ◽  
Random Switching ◽  
Population Ratio ◽  
Non Gaussian ◽  
Time Required ◽  
Parameter Values

In this paper we discuss a parametric sensing strategy employing noise activated escape in a bistable resonator; a system we refer to as the “balanced dynamical bridge.” Noise acting on a bistable system causes random switching between the two metastable states, and the occupation probabilities are very sensitive to system parameters in the weak noise limit. We calculate this sensitivity and the measurement time required when the bridge is employed as a general use detector. The bridge sensitivity is found to be inversely proportional to the noise strength and the measurement time is exponential. We then proceed to consider the dynamical bridge as a detector of non-Gaussian noise. We develop the conditions under which the bridge population ratio is exponentially sensitive only to third and higher moments of a perturbing non-Gaussian noise. As an example, we discuss the implementation of the bridge using a micro- or nano-scale resonator modeled by Duffing’s equation. The locus of parameter values for which the bridge is balanced is presented and we give an example of measuring the statistics of a shot noise process. We also briefly discuss how this class of systems can be employed in micro/nano-scale resonator applications, including mass and force spectroscopy and electron transport.

TRANSIENT PROPERTIES OF A BISTABLE KINETIC SYSTEM WITH TIME-DELAYED FEEDBACK AND NON-GAUSSIAN NOISE: MEAN FIRST-PASSAGE TIME

2008 ◽  
Vol 22 (27) ◽  
pp. 2677-2687 ◽  
Author(s):  
CAN-JUN WANG ◽  
DONG-CHENG MEI
Keyword(s):  
Gaussian Noise ◽  
First Passage Time ◽  
Passage Time ◽  
Delayed Feedback ◽  
Bistable System ◽  
Mean First Passage Time ◽  
First Passage ◽  
The Mean ◽  
Non Gaussian ◽  
Time Delayed Feedback

The transient properties of a bistable system with time-delayed feedback and non-Gaussian noise are investigated. The explicit expressions of the mean first-passage time (MFPT) are obtained. The numerical computations show that the MFPT of the system is affected by the delay time τ, the non-extensive index q and the color noise correlation time τ0. That is, q can induce the MFPT from a complex behavior to a simple monotonous behavior with τ increasing (i.e. from two extrema to no extremum). But with the q increasing, the MFPT has a extremum, which is more large as τ increases.

Methods of mathematical modeling of non-Gaussian random variables quantities and processes

2019 ◽  
pp. 15-21
Author(s):  
V. M. Artyushenko ◽  
V. I. Volovach
Keyword(s):  
Mathematical Modeling ◽  
Gaussian Noise ◽  
Random Variables ◽  
Random Processes ◽  
Mathematical Methods ◽  
Gaussian Random Variables ◽  
One Dimensional ◽  
The One ◽  
Non Gaussian ◽  
Stationary Random Processes

Mathematical methods allowing to model non-Gaussian random variables and processes are considered. The models and description of non-Gaussian correlated processes in the form of generated Gaussian noise are analyzed, as well as the methods of formation of stationary random processes defined by the one-dimensional density distribution of Vero -abilities and the autocorrelation function. Examples of formation of non-Gaussian random variables and processes are given.

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