![]() Here, the so-called mass fluctuation refers to that in many chemical and biological systems, some molecules in the medium have certain adsorption capacity and will randomly absorb and desorb on Brownian particles, so that the mass of the system is no longer a constant, but a random value. In recent years, the SR phenomenon of harmonic oscillator systems with mass fluctuation has attracted considerable attention from many scholars. However, we found that in most previous work, it is generally considered that the external noise of harmonic oscillator caused by the disturbance of system damping or natural frequency, while the external noise caused by the perturbation of the oscillator mass is seldom mentioned. ![]() From the perspective of the model, fluctuations enter the model equation in the form of multiplication, so the study of the SR phenomenon of the harmonic oscillator system essentially belongs to the study of the dynamic behavior of the resonant subsystem under multiplicative external noise. In the past 30 years, a large part of the research on the SR phenomena has been carried out around different dynamical systems and noise forms, and corresponding physical models have been established, respectively. That is, the non-monotonic transformation phenomenon of some functions of system response (such as moment, power spectrum, autocorrelation function, signal to noise ratio, etc.) with some characteristic parameters of the system (such as frequency, excitation amplitude or noise intensity, correlation rate). To avoid ambiguity, the SR mentioned in this paper is the generalized SR without a special explanation. Since then, more and more scholars have paid attention to the theoretical and experimental researches on SR, which makes it gradually become a hot topic in the field of stochastic dynamics. Contrary to the common knowledge that noise is harmful, the SR phenomenon shows that random disturbance (noise) can produce a cooperative effect under certain conditions, it can realize the transfer of noise energy to signal energy, and it thus may strengthen the system output. The term of SR was proposed by Benzi and Nicolis to explain the climatic mechanics of periodic glaciers in the 1980s. For example, there is a transition from bimodal resonance to unimodal resonance between the amplitude and the driving frequency under different fractional orders.Īs 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. Furthermore, the mass fluctuation noise, modulation noise, and the fractional order work together, producing more complex dynamic phenomena than the integral-order system. 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. 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 mass fluctuation noise is modeled as dichotomous noise and the memory of viscous media is characterized by fractional power kernel function. The stochastic resonance (SR) of a second-order harmonic oscillator subject to mass fluctuation and periodic modulated noise in viscous media is studied.
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