Effects of the Shape of Periodic Forces on Stochastic Resonance

Abstract

We study the influence of the shapes of three different external periodic forces on the stochastic resonance phenomenon in multiple potential well systems with Gaussian noise. We consider as external periodic forces the sine wave, the modulus of sine wave and the rectified sine wave. The systems of our interest are two coupled overdamped anharmonic oscillators and the Duffing oscillator. For fixed values of the parameters, when the intensity D of the external noise is varied, the systems with these periodic forces separately are found to exhibit stochastic resonance. Certain similarities and differences are found in the characteristics of these statistical measures such as signal-to-noise ratio (SNR), response amplitude (Q), time series plot, mean residence time τMR in the potential wells and the distribution P of the normalized residence time for these different forces. Especially, the time series plot at the maximum SNR shows an almost periodic switching between the potential wells for the sine force which is not observed for the other two forces. In the noise-induced intermittent dynamics, τMR is the same in different wells for the sine force, whereas it is different in different wells for the other two forces for each value of the noise intensity D. Further, variation of τMR with D, the value of τMR at the resonance and the distribution P show different features for the different types of forces. We present a detailed comparative study and explanation for the similarities and differences observed in the stochastic resonance dynamics.

Analysis of vibrational resonance in a quintic oscillator

“…The vibrational resonance phenomenon has been found in the double-well Duffing oscillator, [2][3][4] spatially extended, 5 excitable 6 systems, an overdamped bistable system, [7][8][9] and overdamped two-coupled anharmonic oscillators. 10,11 The effects of noise on vibrational resonance have also been ana-lyzed in certain systems. 7,12,13 Experimental evidence of vibrational resonance was found in a bistable vertical cavity surface emitting laser 13 and an optical system.…”

Research on Extraction Technology of Gear System Failure Diagnosis based on Stochastic Resonance

“…The output SNR of the system of nonlinear stochastic resonance is 0 0 10 log( ( ) / ( )) SNRout S w N w = When nonlinear stochastic resonance system is the best stage, the corresponding SNR output is also to the maximum. Adaptive stochastic resonance system design based on the SNR parameters of the system output [5]. That is, whether to achieve maximum SNR of the nonlinear system output to determine whether the system achieve optimal stochastic resonance state, use a LRS dynamic regulation of nonlinear stochastic resonance parameters a, u, thereby regulating the barrier of nonlinear stochastic resonance system U ∆ .The following analytical expression is for the adaptive stochastic resonance algorithm.…”

Stochastic Resonance and Bifurcation of Order Parameter in a Coupled System of Underdamped Duffing Oscillators

“…1 shows an application example of SR in image detection. Several methods have been presented to enhance the resonance effects for various applications, for instance, altering the shape of the potential and periodic forces of a single system [Wio & Bouzat, 1999;Gandhimathi et al, 2008;Arathi et al, 2011] or coupling several subsystems to obtain an enhanced collective response [Jung et al, 1992;Lindner et al, 1995;Morillo et al, 1995;Kang & Jiang, 2009;Nicolis & Nicolis, 2017]. Specifically, the earliest investigation on the collective response can be dated back to the work based on nonlinear master equations [Jung et al, 1992].…”