Trichotomous noise induced stochastic resonance in a fractional oscillator with random damping and random frequency

Abstract

Several corrections were not applied at the proofreading stage. The Production team regrets the errors, and presents the corrections here. These corrections do not aect the scientific outcomes of the paper.(1) On page 6, there should be a '.' at the end of the last one of the equation (6).(2) On page 6, there should be a '.' at the end of the equation (7).(3) On the 6th row of page 7, there is an extra x˙ in the expression of d 34 .(4) On the 7th row of page 7, ' and x 1 (0), x 2 (0) and x 3 (0) are the initial conditions'.should be corrected into 'and x 1 (0), x 2 (0), x 3 (0), x˙0 1 ( ), x˙0 2 ( ), x˙0 3 ( ) are the initial conditions'.

A New Dynamical Method for Bearing Fault Diagnosis Based on Optimal Regulation of Resonant Behaviors in a Fluctuating-Mass-Induced Linear Oscillator

“…Previous studies have noted that bona fide SR behavior widely exists in this type of LO system [31,32,34,36], that is, as the driving frequency f increases, the output periodic component of system stationary response non-monotonously decreases with single or double peaks, especially for high-frequency driving signal. It becomes much weaker, and completely submerges in the background noise.…”

“…However, all these dynamical methods mentioned above were based on nonlinear systems, in which nonlinearity, periodicity and random force were generally regarded as the basic elements for generating classical SR behaviors, but in recent years, many studies on wide-sense SR phenomena have overturned this view, and expanded it to linear oscillator (LO) by introducing additive and multiplicative noise, i.e., linear noisy oscillators with random fluctuations on damping [30,31], frequency [32][33][34], or mass [35,36]. Particularly, random-mass systems were first proposed in chemical and biological background, where the surrounding molecules not only collide with the oscillator but may also adhere to it, thereby changing its mass [37].…”

Bearing fault diagnosis based on the active energy conversion of generalized stochastic resonance in fluctuating-frequency linear oscillator

“…All the methods mentioned above follow the framework of the classical SR theory with nonlinearity, periodicity and random force as the basic elements, but this view has been overturned by many studies on generalized SR (GSR) phenomena in recent years, and it is extended it to linear Langevin system by introducing multiplicative noises [27][28][29][30][31][32][33][34]. Thus, Chen et al [35] explored the bearing fault diagnosis method based on a fluctuating-mass linear oscillator, where the internal randomness acting upon the second-order term was introduced to regulate the dynamical behaviors.…”

Homoclinic and heteroclinic chaos in nonlinear systems driven by trichotomous noise

“…For example, Mankin et al investigated trichotomous-noise-induced transitions [20] and explored the stochastic resonance phenomenon in some linear systems subjected to trichotomous noise. [25][26][27] The cases of stochastic resonance of a linear oscillator with random damping parameter, [28] several fractional oscillators, [29][30][31] the coupled underdamped bistable systems [32] and the FitzHugh-Nagumo neuron model [33] driven by trichotomous noise have also been analyzed. Zhong et al [30] studied two different forms of the generalized stochastic resonance phenomena versus trichotomous noise intensity.…”