Trichotomous Noise Induced Resonance Behavior for a Fractional Oscillator with Random Mass

Abstract

We investigate the stochastic resonance (SR) phenomenon in a fractional oscillator with random mass under the external periodic force. The fluctuations of the mass are modeled as a trichotomous noise. Applying the Shapiro-Loginov formula and the Laplace transform technique, we obtain the exact expression of the first moment of the system. The non-monotonic behaviors of the spectral amplification (SPA) versus the driving frequency indicate that the bona fide SR appears. The necessary and sufficient conditions for the emergence of the generalized stochastic resonance phenomena on the noise flatness and on the noise intensity in the particular case of = ω 0 , v → 0 are established. Particularly, the hypersensitive response of the SPA to the noise intensity is found, which is previously reported and believed to be absent in the case of dichotomous noise.

Stationary Response of a Kind of Nonlinear Stochastic Systems with Variable Mass and Fractional Derivative Damping

“…Thus, this variable mass phenomenon should be described as a stochastic process. The initial models of random variable mass oscillator were always simplified by dichotomous or trichotomous noise [13][14][15][16][17]. However, the variable mass modeling method based on dichotomous or trichotomous noise limits the mass change within two or three states, which can not fully show the randomness of the variable mass of micro-devices.…”

“…Then it gives ẏ1 = y 2 m e +σξ m (t) , ẏ2 = −ζ e y 2 m e +σξ m (t) − g e (y 1 ) + ε f (y 1 )ξ f (t). (16) Due to the mass disturbance σξ m (t), stochastic averaging method can not be employed in System (16). However, if the mass disturbance σξ m (t) is small enough, the following approximated equation is obtained based on the Taylor expansion technique,…”

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.…”

“…[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. For the stochastic chaos, several studies have focused on systems induced by Gaussian noise [34,35] or Poisson noise.…”

The Stochastic Resonance Behaviors of a Generalized Harmonic Oscillator Subject to Multiplicative and Periodically Modulated Noises

“…Nowadays, the GLE driven by a fractional Gaussian noise (fGn) [46] with a power-law friction kernel is extensively used for modeling anomalous diffusion processes. For instance, in the study on dynamics of single-molecule when the electron transfer (ET) was used to probe the conformational fluctuations of single-molecule enzyme, the distance between the ET donor and acceptor can be modeled well through a GLE driven by an fGn [47][48][49][50][51][52][53][54]. Besides, Viñales and Despósito have introduced a novel noise whose correlation function is proportional to a Mittag-Leffler function, which is called the Mittag-Leffler noise (M-Ln) [55][56][57].…”