Stochastic resonance of a damped oscillator with frequency fluctuation driven by a periodic external force

<正>Considering a damped linear oscillator model subjected to a white noise with an inherent angular frequency and a periodic external driving force,we derive the analytic expression of the first moment of output response,and study the stochastic resonance phenomenon in a system.The results show that the output response of this system behaves as a simple harmonic vibration,of which the frequency is the same as the external driving frequency,and the variations of amplitude with the driving frequency and the inherent frequency present a bona fide stochastic resonance.     

Stochastic resonance in with additive noises a stochastic bistable system and square-wave signal

<正>This paper considers the stochastic resonance in a stochastic bistable system driven by a periodic square-wave signal and a static force as well as by additive white noise and dichotomous noise from the viewpoint of signal-to-noise ratio.It finds that the signal-to-noise ratio appears as stochastic resonance behaviour when it is plotted as a function of the noise strength of the white noise and dichotomous noise,as a function of the system parameters,or as a function of the static force.Moreover,the influence of the strength of the stochastic potential force and the correlation rate of the dichotomous noise on the signal-to-noise ratio is investigated.     

Stochastic resonance in a time-delayed bistable system subject to multiplicative and additive noise

This paper investigates the stochastic resonance in a time-delayed bistable system subjected to multiplicative and additive white noise and asymmetric dichotomous noise.Under the adiabatic approximation condition,the expression of the signal-to-noise ratio (SNR) is obtained.It finds that the SNR is a non-monotonic function of the delayed times,of the amplitude of the driving square-wave signal,as well as of the asymmetry of the dichotomous noise.In addition,the SNR varies non-monotonously with the intensities of the multiplicative and additive noise as well as the system parameters.Moreover,the SNR depends non-monotonically on the correlate rate of the dichotomous noise.     

Stochastic Resonance in a Time-Delayed Mono-Stable System with Multiplicative and Additive Noise

The stochastic resonance （SR） in a time-delayed mono-stable system driven by multiplicative white noise, additive white noise, additive dichotomous noise as well as a periodic square-wave signal is considered from the view of the signal-to-noise ratio （SNR）. It is found that the SNR increases monotonically with the increase of the delay time. The SNR exhibits the SR behavior when it is plotted as a function of intensities of the noises, displaying the asymmetry of the dichotomous noise. The SNR varies non-monotonically with the increase of the system parameter and the amplitude of the input square-wave signal.     

Entropic stochastic resonance in a confined structure driven by dichotomous noise and white noises

The entropic stochastic resonance(ESR) in a confined system subjected to dichotomous noise and white noise and driven by a periodic sinusoidal force along the x axis of the structure and a time-dependent force in the declining direction,is investigated.Under the adiabatic approximation condition and based on the two-state theory,the expression of the output signal-to-noise ratio(SNR) is obtained.The results show that the SNR is a non-monotonic function of the strengths of dichotomous noise,white noise,and correlated strength of correlated noise.In addition,the SNR varies non-monotonically with the increase of the shape parameters of the confined structure,and also with the increase of the constant force along the y axis of the structure.The influence of the correlation rate of the dichotomous noise,and that of the frequency of the periodic force on the SNR are discussed.     

Frequency Resonance in Stochastic Systems

The phenomenon of frequency resonance,which is usually related to deterministic systems.is investigated in stochastic systems.We show that for those autonomous systems driven only by white noise,if the output power spectrum exhibits a nonzero peak frequency,then applying a periodic signal just on this noise-induced central frequency can also induce a resonance phenomenon,which we call the frequency stochastic resonance.The effect of such a resonance in a coupled stochastic system is shown to be much better than that in a single-oscillator system.     

Stochastic Resonance in a Bistable System Subject to Non-Gaussian and Gaussian Noises

In this paper, we consider the phenomenon of stochastic resonance （SR） in a quartic bistable system under the simultaneous action of a multiplicative non-Gaussian and an additive Gaussian noises and a weak periodic signal. The expression of the signal-to-noise ratio R is derived by applying the two-state theory in adiabatic limit. We discuss the effects of the parameter q indicating the departure of the non-Gaussian noise from the Gaussian noise, the correlation time r of the non-Gaussian noise, and coupling intensity A between two noise terms on the stochastic resonance. It is found that the signM-to-noise ratio of the system, as a function of the additive noise intensity, undergoes the transition from having one peak to having two peaks, and then to having one peak again when the parameter q or the noise correlation time τ is increased. The parameter q and τ play opposite roles in the SR of the system.     

Stochastic resonance and nonequilibrium dynamic phase transition of Ising spin system driven by a joint external field

The dynamic response and stochastic resonance of a kinetic Ising spin system （ISS） subject to the joint action of an external field of weak sinusoidal modulation and stochastic white-nolse are studied by solving the mean-field equation of motion based on Glauber dynamics. The periodically driven stochastic ISS shows that the characteristic stochastic resonance as well as nonequilibrium dynamic phase transition （NDPT） occurs when the frequency ω and amplitude h0 of driving field, the temperature t of the system and noise intensity D are all specifically in accordance with each other in quantity. There exist in the system two typical dynamic phases, referred to as dynamic disordered paramagnetic and ordered ferromagnetic phases respectively, corresponding to a zero- and a unit-dynamic order parameter. The NDPT boundary surface of the system which separates the dynamic paramagnetic phase from the dynamic ferromagnetic phase in the 3D parameter space of ho-t-D is also investigated. An interesting dynamical ferromagnetic phase with an intermediate order parameter of 0.66 is revealed for the first time in the ISS subject to the perturbation of a joint determinant and stochastic field. The intermediate order dynamical ferromagnetic phase is dynamically metastable in nature and owns a peculiar characteristic in its stability as well as the response to external driving field as compared with a fully order dynamic ferromagnetic phase.     

Stochastic Resonance in a Single-Ion Nonlinear Mechanical Oscillator

Stochastic resonance is a counterintuitive phenomenon amplifying the weak periodic signal by application of external noise. We demonstrate the enhancement of a weak periodic signal by stochastic resonance in a trappedion oscillator when the oscillator is excited to the nonlinear regime and subject to an appropriate noise. Under the full control of the radio-frequency drive voltage, this amplification originates from the nonlinearity due to asymmetry of the trapping potential, which can be descri...