Stochastic resonance in the overdamped fractional oscillator subject to multiplicative dichotomous noise

Abstract

With the increasingly deep studies in physics and technology, the behavior of fractional oscillators have become the focus of scientific research. In this paper, the stochastic resonance (SR) mechanism of the overdamped fractional oscillator subject to multiplicative dichotomous noise is extensively investigated. Using the Shapiro–Loginov formula and the Laplace transformation technique, the exact expression for complex susceptibility is obtained. Resorting to numerical simulations, the SR phenomenon of the overdamped fractional oscillator is studied. Especially, the frequency of the external periodic force that induces multiresonance.

Collective stochastic resonance behaviors of two coupled harmonic oscillators driven by dichotomous fluctuating frequency*

“…[4][5][6][7][8][9][10][11][12][13] However, many recent investigations show that SR can also occur in linear systems with multiplicative colored noise. [14][15][16][17][18][19][20][21][22][23][24] As a classical model, harmonic oscillators [25] are widely used to describe various natural phenomena. Thus, the research on harmonic oscillators have draw more and more attention.…”

Collective behaviors of two coupled harmonic oscillators driven by different frequency fluctuations with fractional damping

“…Nonlinearity together with weak periodic signals and noise are considered necessary conditions for the emergence of SR; thus, for a long time, SR investigations mainly concentrated on nonlinear systems with additive noise [8][9][10][11][12][13][14][15][16]. However, many recent studies have pointed out that SR can also occur in linear systems stimulated by multiplicative colored noise [7,[17][18][19][20][21][22][23][24][25][26].…”

Trichotomous noise induced resonance behavior of two coupled harmonic oscillators with fluctuating mass

“…After nearly 40 years of unremitting research, the SR phenomena has been observed in many linear systems for the system nonlinearity is produced by multiplicative colored noise [16][17][18][19][20][21][22][23][24][25][26]. In fact, the multiplicative noise breaks the symmetry of the parabolic potential profile.…”