Stochastic resonance of fractional-order Langevin equation driven by periodic modulated noise with mass fluctuation

Shan Yang,Mou Deng,Ruibin Ren

doi:10.1186/s13662-020-2492-7

Shan Yang, Mou Deng + Show 1 more

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https://doi.org/10.1186/s13662-020-2492-7

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Abstract

The stochastic resonance (SR) of a second-order harmonic oscillator subject to mass fluctuation and periodic modulated noise in viscous media is studied. The mass fluctuation noise is modeled as dichotomous noise and the memory of viscous media is characterized by fractional power kernel function. By using the Shapiro–Loginov formula and Laplace transform, we got the analytical expression of the first moment of the steady-state response and studied the relationship between the system response and the system parameters in the long-time limit. The simulation results show the non-monotonic dependence between the response amplitude and the input signal frequency, noise parameters of the system, etc, which indicates that the bona fide resonance and the generalized SR phenomena appear. Furthermore, the mass fluctuation noise, modulation noise, and the fractional order work together, producing more complex dynamic phenomena than the integral-order system. For example, there is a transition from bimodal resonance to unimodal resonance between the amplitude and the driving frequency under different fractional orders.

Highlights

As the research frontier of the statistical physics and the stochastic dynamical system, the stochastic resonance (SR) driven by fluctuation and periodic signal recently become a popular research direction [1,2,3,4]
Contrary to the common knowledge that noise is harmful, the SR phenomenon shows that random disturbance can produce a cooperative effect under certain conditions, it can realize the transfer of noise energy to signal energy, and it may strengthen the system output
3 System model and its solution A fractional harmonic oscillator model with mass fluctuation driven by periodic modulation noise, can be described by the fractional Langevin equation as follows: m + ξ (t) d2x(t) dt2

Summary

Introduction

As the research frontier of the statistical physics and the stochastic dynamical system, the stochastic resonance (SR) driven by fluctuation and periodic signal recently become a popular research direction [1,2,3,4]. One of the main works of this paper will be to consider the SR phenomenon of harmonic oscillator with mass fluctuation under the effect of periodic modulation noise.

Results

Conclusion