Trajectory (Phase) Selection in Multistable Systems: Stochastic Resonance, Signal Bias, and the Effect of Signal Phase

1995 ◽  
Vol 74 (20) ◽  
pp. 3955-3958 ◽  
Author(s):  
Weiming Yang ◽  
Mingzhou Ding ◽  
Hu Gang
Keyword(s):  
Stochastic Resonance ◽  
Resonance Signal ◽  
Signal Phase ◽  
Phase Selection ◽  
Multistable Systems

scholarly journals Bistable systems with stochastic noise: virtues and limits of effective one-dimensional Langevin equations

2012 ◽  
Vol 19 (1) ◽  
pp. 9-22 ◽  
Author(s):  
V. Lucarini ◽  
D. Faranda ◽  
M. Willeit
Keyword(s):  
Stochastic Resonance ◽  
Ad Hoc ◽  
Thermohaline Circulation ◽  
Statistical Properties ◽  
Langevin Equations ◽  
Oceanic Circulation ◽  
One Dimensional ◽  
Bistable Systems ◽  
Box Models ◽  
Multistable Systems

Abstract. The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies, using simple box models of the oceanic circulation and choosing as observable the strength of the thermohaline circulation. We study the statistical properties of the transitions between the two modes of operation of the thermohaline circulation under symmetric boundary forcings and test their agreement with simplified one-dimensional phenomenological theories. We extend our analysis to include stochastic resonance-like amplification processes. We conclude that fitted one-dimensional Langevin models, when closely scrutinised, may result to be more ad-hoc than they seem, lacking robustness and/or well-posedness. They should be treated with care, more as an empiric descriptive tool than as methodology with predictive power.

STOCHASTIC RESONANCE SIGNAL PROCESSOR: PRINCIPLE, CAPACITY ANALYSIS AND METHOD

2007 ◽  
Vol 17 (02) ◽  
pp. 631-639 ◽  
Author(s):  
SHUIFA SUN ◽  
SAM KWONG
Keyword(s):  
Stochastic Resonance ◽  
Additive White Gaussian Noise ◽  
Pulse Amplitude ◽  
Bit Rate ◽  
Resonance Signal ◽  
Noise Simulation ◽  
Error Ratio ◽  
Bit Error Ratio ◽  
Base Band ◽  
Signal Processor

In this letter, a signal processor based on the bistable aperiodic stochastic resonance (ASR), that can be used to detect the base-band binary pulse amplitude modulation (PAM) signal transmitting over an additive white Gaussian noise (AWGN) channel, is studied. The principle of the ASR signal processor is analyzed and the information capacity of such a communication system is evaluated by the Bit Error Ratio (BER) and the bit rate, according to the well-known Shannon information theory. The roles played by the noise on this capacity are analyzed. It is observed that keeping the bit rate unchanged we can neither decrease BER nor increase the bit rate and keep BER unchanged by adjusting the density of the noise. Simulation results also agree well with this observation. In addition, a statistical method to improve the performance of the system is proposed with theory and experiment.

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