Stochastic resonance in a tunnel diode in the presence of white or coloured noise

Multiple stochastic and inverse stochastic resonances with transition phenomena in complex corporate financial systems

This study examines the role of periodic information, the mechanism of influence, stochastic resonance, and its controllable analysis in complex corporate financial systems. A stochastic predator-prey complex corporate financial system model driven by periodic information is proposed. Additionally, we introduce signal power amplification to quantify the stochastic resonance phenomenon and develop a method for analyzing stochastic resonance in financial predator-prey dynamics within complex corporate financial systems. We optimize a simplified integral calculation method to enhance the proposed model's performance, which demonstrates superiority over benchmark models based on empirical evidence. Based on stochastic simulations and numerical calculations, we can observe multiple stochastic and multiple inverse stochastic resonances. Furthermore, variations in initial financial information, periodic information frequency, and corporate growth capacity induced stochastic resonance and inverse stochastic resonance. These variations also led to state transitions between the two resonance behaviors, indicating transition phenomena. These findings suggest the potential for regulating and controlling stochastic and inverse stochastic resonance in complex corporate finance, enabling controllable stochastic resonance behaviors.

Debye Brownian oscillator and Debye-type noise: A series solution versus Monte Carlo simulation

For the Debye Brownian oscillator, we present a series solution to the generalized Langevin equation describing the motion of a particle. The external potential is considered to be a harmonic potential and the spectral density of driven noise is a hard cutoff at high finite frequencies. The results are in agreement with both numerical calculations and Monte Carlo simulations. We demonstrate abnormal weak ergodic breaking; specifically, the long-time average of the observable vanishes but the corresponding ensemble average continues to oscillate with time. This Debye Brownian oscillator does not arrive at an equilibrium state and undergoes underdamped-like motion for any model parameter. Nevertheless, ergodic behavior and equilibrium can be recovered concurrently using a strong bound potential. We give an understanding of the behavior as being the consequence of discrete breather modes in the lattices similar to the formation of an additional periodic signal. Furthermore, we compare the results calculated by cutting off separately the spectral density and the correlation function of colored noise.

Observation of stochastic resonance in a liquid-crystal light valve with optical feedback induced by colored noise in the driving voltage

Stochastic resonance is a noise phenomenon that benefits applications such as pattern formation, neural systems, microelectromechanical systems, and image processing. This study experimentally clarifies that the orientation of the liquid crystal molecules was switched between two stable positions when stochastic resonance was induced by colored noises in a liquid crystal light valve with optical feedback. Ornstein-Uhlenbeck and dichotomous noises were used for colored noise, and the noise was applied to the drive voltage of the liquid crystal light valve. The signal-to-noise ratio was measured with respect to changes in the noise type, noise intensity, and autocorrelation time of the noise. It was found that typical stochastic resonance was observed with a noise autocorrelation time of approximately 20 ms or more for both noise types, and dichotomous noise further enhanced the stochastic resonance compared to the Ornstein-Uhlenbeck noise. This suggests that it is possible to maximize stochastic resonance in a liquid crystal light valve by optimizing the conditions of colored noise.

Entropic stochastic resonance enables trapping under periodic confinement: a Brownian-dynamics study

Entropically mediated phenomena are of emerging interest as a driving force for microscale and nanoscale transport, but their underlying stochastic nature makes them challenging to rationally manipulate and control. Stochastic resonance offers an intriguing avenue to overcome these difficulties by establishing a clear connection between the system response (the output) and an externally imposed driving force (the input). Previous studies have generally adopted a signal-processing viewpoint to classify the output in terms of a signal-to-noise ratio, but this link does not convey information that is immediately useful to infer parameters relevant to transport. Here we address this issue by applying Brownian-dynamics simulations to elucidate the residence time distribution encountered by a particle as it travels through a channel incorporating periodic constrictions. A sinusoidal longitudinal driving force is applied with a superimposed continuous orthogonal component, making it possible to identify frequency and amplitude conditions where temporal coherence with the particle's motion can be achieved. This resonant state reflects a synergistic combination of geometry and driving force that can be exploited to confine species at discrete locations, offering possibilities for directed manipulation.

Reverse resonance in stock prices of financial system with periodic information

We investigate the stochastic resonance of the stock prices in a finance system with the Heston model. The extrinsic and intrinsic periodic information are introduced into the stochastic differential equations of the Heston model for stock price by focusing on the signal power amplification (SPA). We find that for both cases of extrinsic and intrinsic periodic information a phenomenon of reverse resonance emerges in the behaviors of SPA as a function of the system and external driving parameters. Moreover, in both cases, a phenomenon of double reverse resonance is observed in the behavior of SPA versus the amplitude of volatility fluctuations, by increasing the cross correlation between the noise sources in the Heston model.

Stationary energy probability density of oscillators driven by a random external force

We derive rigorous analytical results for the stationary energy probability density function of linear and nonlinear oscillators driven by additive Gaussian noise. Our study focuses on two cases: (i) a harmonic oscillator subjected to Gaussian colored noise with an arbitrary correlation function and (ii) nonlinear oscillators with a general potential driven by Gaussian white noise. We also derive analytical expressions for the stationary moments of the energy and investigate the partition of the mean energy between kinetic and potential energy. To illustrate our general results, we consider specifically the case of exponentially correlated noise for (i) and power-law and bistable potentials for (ii). Our theoretical results are substantiated by Langevin simulations.

Chaos supported stochastic resonance in a metal-ferroelectric-semiconductor heterostructure

An experimental study is presented on a complex nonlinear system showing a particular type of dynamics that can be interpreted as stochastic resonance. The system consists of a metal-ferroelectric-semiconductor structure, which plays the role of a nonlinear element in an electric circuit with linear resistance, inductance, and capacitance connected in series (RLC series circuit) driven externally by a high-amplitude harmonic voltage source. The system presents various kinds of nonlinear behavior, of which the simplest, consisting of a period-doubling evolution to chaos, is of interest to this study. The broadband intrinsic chaos emerging after a period-doubling sequence exists for a large range of frequencies of the driving voltage. The appearance of the chaotic dynamics is associated with the promotion of a low-frequency harmonic spectral component. This is interpreted as stochastic resonance with intrinsic chaos replacing noise, the usual variable in regular SR.

Overview: Unsolved problems of noise and fluctuations

Noise and fluctuations are at the seat of all physical phenomena. It is well known that, in linear systems, noise plays a destructive role. However, an emerging paradigm for nonlinear systems is that noise can play a constructive role-in some cases information transfer can be optimized at nonzero noise levels. Another use of noise is that its measured characteristics can tell us useful information about the system itself. Problems associated with fluctuations have been studied since 1826 and this Focus Issue brings together a collection of articles that highlight some of the emerging hot unsolved noise problems to point the way for future research. (c) 2001 American Institute of Physics.

Linear and nonlinear experimental regimes of stochastic resonance

We investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode. The experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an interval of values spanning several orders of magnitude. We observe both a regime described by the linear-response theory and the nonlinear deviation from it. In the nonlinear regime we detect saturation of the power spectral density of the output signal detected at the frequency of the modulating signal and a dip in the noise level of the same spectral density. When these effects are observed we detect a phase and frequency synchronization between the stochastic output and the deterministic input.

Nonlinear stochastic resonance: the saga of anomalous output-input gain

We reconsider stochastic resonance (SR) for an overdamped bistable dynamics driven by a harmonic force and Gaussian noise from the viewpoint of the gain behavior, i.e., the signal-to-noise ratio (SNR) at the output divided by that at the input. The primary issue addressed in this work is whether a gain exceeding unity can occur for this archetypal SR model, for subthreshold signals that are beyond the regime of validity of linear response theory: in contrast to nondynamical threshold systems, we find that the nonlinear gain in this conventional SR system exceeds unity only for suprathreshold signals, where SR for the spectral amplification and/or the SNR no longer occurs. Moreover, the gain assumes, at weak to moderate noise strengths, rather small (minimal) values for near-threshold signal amplitudes. The SNR gain generically exhibits a distinctive nonmonotonic behavior versus both the signal amplitude at fixed noise intensity and the noise intensity at fixed signal amplitude. We also test the validity of linear response theory; this approximation is strongly violated for weak noise. At strong noise, however, its validity regime extends well into the large driving regime above threshold. The prominent role of physically realistic noise color is studied for exponentially correlated Gaussian noise of constant intensity scaling and also for constant variance scaling; the latter produces a characteristic, resonancelike gain behavior. The gain for this typical SR setup is further contrasted with the gain behavior for a "soft" potential model.

Experimental investigation of resonant activation

We experimentally investigate the escape from a metastable state over a fluctuating barrier of a physical system. The system is switching between two states under electronic control of a dichotomous noise. We measure the escape time and its probability density function as a function of the correlation rate of the dichotomous noise in a frequency interval spanning more than four frequency decades. We observe resonant activation, namely a minimum of the average escape time as a function of the correlation rate. We detect two regimes in the study of the shape of the escape time probability distribution: (i) a regime of exponential and (ii) a regime of nonexponential probability distribution.