Amplification of weak signals via the non-adiabatic regime of stochastic resonance in a bistable dynamical system with time delay

Abstract

The non-adiabatic regime of stochastic resonance (SR) in a bistable system with time delay, an additive white noise and a periodic signal was investigated. The signal power amplification η was employed to characterize the SR of the system. The simulation results indicate that (i) in the case of intermediate frequency of the periodic signal, the typical behavior of SR is lowered monotonically by increasing the delay time τ ; in the case of large , τ weakens the SR behavior and then enhances it, with a non-monotonic behavior as a function of time delay; (ii) time delay induces SR when A is above the threshold, whereas no such resonance exists in the absence of time delay; (iii) time delay induces a transition from bimodal to unimodal configuration of η; (iv) varying the particular form of time delay results in different phenomena.

Is the High-Frequency Signal Necessary for the Resonance in the Delayed System?

“…They made the resonance occur by the cooperation of the noise and the delay time. [23] According to the nonlinear vibration theory, the response of the system contains a set of frequency components. Hence, the response of the system can be described in the form…”

Stochastic resonance induced by the memory of a random delay

“…where λ is the strength of the delayed feedback, the function φ(t) is the initial function and A cos(2π f t) is the periodic excitation. Equation (3) serves as the simplest but most widely used prototypical model for manifesting the phenomenon of SR [26][27][28].…”

Periodic fault signal enhancement in rotating machine vibrations via stochastic resonance

“…SR is widely utilized in weak signal detection (WSD) areas due to its distinct merits (Du and Mei, 2011;Almog et al, 2007;Chen et al, 2007). Specially, many SR-based WSD studies focused on rotating machine fault diagnosis (Ompusunggu et al, 2013;Lei et al, 2013c;Shi et al, 2014;Li et al, 2013b;Lei et al, 2013a;Zhao et al, 2013;Hu et al, 2003;Leng et al, 2006).…”