Stochastic Resonance Behavior Research Articles

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.

Parameter influence analysis of stochastic resonance and stochastic P-bifurcation for the shape-memory alloy laminate

This paper investigates the transverse vibration of an axially moving shape-memory alloy (SMA) fiber hybrid laminations under the combined action of transverse harmonic excitation and stochastic disturbance. Considering the shape memory alloy (SMA) fiber volume fraction random field, the kinetic energy and strain potential energy of SMA laminates are solved, and the axial motion equation of SMA laminates is derived according to Hamilton principle, a non-dimensional differential equation of the transverse vibration of the axially moving SMA laminated plates is obtained by adopting the Galerkin integral method. Considering the volume-fraction stochastic field, the stochastic natural vibration of a SMA laminate is analyzed. Considering the stochastic resonance of the SMA laminate under the action of Gaussian white noise and harmonic excitation, the effects of geometric parameters, physical parameters of materials, and temperature on the stochastic resonance behavior of the SMA laminate is analyzed. Finally, the effect of the stochastic P-bifurcation phenomenon of the parameters on the steady-state response of the SMA laminate is analyzed.

Stochastic resonance in 2D materials based memristors

Stochastic resonance is an essential phenomenon in neurobiology, it is connected to the constructive role of noise in the signals that take place in neuronal tissues, facilitating information communication, memory, etc. Memristive devices are known to be the cornerstone of hardware neuromorphic applications since they correctly mimic biological synapses in many different facets, such as short/long-term plasticity, spike-timing-dependent plasticity, pair-pulse facilitation, etc. Different types of neural networks can be built with circuit architectures based on memristive devices (mostly spiking neural networks and artificial neural networks). In this context, stochastic resonance is a critical issue to analyze in the memristive devices that will allow the fabrication of neuromorphic circuits. We do so here with h-BN based memristive devices from different perspectives. It is found that the devices we have fabricated and measured clearly show stochastic resonance behaviour. Consequently, neuromorphic applications can be developed to account for this effect, that describes a key issue in neurobiology with strong computational implications.

Effects of time delay on the collective behavior of globally coupled harmonic oscillators with fluctuating frequency

In the viscoelastic environment, coupling forces between particles often play an essential role. Due to the time delay in the transmission of coupling forces, this paper focuses on investigating the effects of time delay on the collective behaviors of coupled harmonic oscillators, including synchronization, stability, and stochastic resonance. Firstly, we establish a time delay decoupling formula that can complete the accurate solution of the model under a large delay, thus breaking the limitation of previous small delay approximation methods. Secondly, the statistical synchronization between particles is derived, which means the mean-field behavior of the system can be studied through single-particle behavior. Thirdly, the system’s stability condition is given, demonstrating that the stability region expands with increasing time delay. Finally, the output response amplitude gain of the system is obtained, and then the stochastic resonance behavior of the system is studied. In the small delay region, noise competes with the ordered driving force, resulting in the classical stochastic resonance (CSR) behavior consistent with previous research findings. In the large delay region, periodic matching between the time delay and driving frequency gives rise to parameter-induced stochastic resonance (PSR) behavior, which has not been observed in previous studies.

Influence of colored cross-correlated noise on stochastic resonance for an underdamped bistable system subjected to multiplicative and additive noises

The stochastic resonance (SR) behavior for an underdamped bistable system with colored cross-correlated noise between multiplicative and additive noise is investigated. The stationary probability density is obtained under the condition of the detailed balance. The expressions for the signal-to-noise ratios (SNRs) for two initial states is deduced by applying two-state theory under the adiabatic condition. The analysis result indicates that the SR phenomenon takes place when the SNRs vary with the coupling strength and the correlation time of the cross-correlated noise. Double SR phenomenon occurs on SNRs’ curves with the increase of the strength of the additive noise. One resonance peak exists when the SNRs change with the damping coefficient and with the intensity of the multiplicative noise.

Generalized stochastic resonance in a time-delay fractional oscillator with damping fluctuation and signal-modulated noise

In this study, we propose a time-delayed fractional oscillator (FO) subjected to damping fluctuation and signal-modulated noise, and investigate the generalized stochastic resonance (GSR) behaviors. By using (fractional) Shapiro–Loginov formula and Laplace transform, we obtain the first-order moment of system stationary state response, and the output amplitude gain (OAG). Based on the analytical results, it is observed that the GSR behaviors widely exist in the system, and they can be effectively controlled by the system parameters, including driving frequency, noise parameters, fractional order and time delay. It is also demonstrated that fractional order and time delay are two effective dimensions to regulate the GSR intensity under different parameter conditions, and the diversity of GSR behaviors mainly depends on the fractional order.

Abnormal thermal conduction and stochastic resonance phenomenon in a finite lattice system

This paper studies the thermal conduction of Frenkel–Kontorva (FK)-ϕ4 lattices with the finite number of atoms under a periodic force. Through numerical simulations, we find that in the thermal conduction of non-linear lattices, external periodic signals can act in conjunction with noise to create stochastic resonance behaviors and that some adjustable dynamical parameters, such as the onsite potential of the FK and ϕ4 lattices, the amplitude and frequency of external periodic signals, can regulate heat flux. Our study results can provide a sufficient theoretical basis for the fabrication of thermal devices and the control and utilization of thermal energy.

The adaptive bearing fault diagnosis based on optimal regulation of generalized SR behaviors in fluctuating-damping induced harmonic oscillator

Stochastic resonance (SR) has been widely used in bearing fault diagnosis due to the noise-assisted enhancement principle of weak fault signal. The purpose of this paper is to cast off the basic constraint of nonlinearity and extend the classical SR-based nonlinear methods to a new linear Langevin system of fluctuating-damping linear oscillator (FDLO), and to introduce the generalized scale transformation (GST) to make it more suitable for processing fault features. By analyzing the system stationary response, it is found that the proposed GST-FDLO system displays a rich variety of generalized SR (GSR) behaviors generated by the active synergy between internal regulation and external input signal. Furthermore, the GSR-based energy conversion mechanism is investigated to reveal the effects of different parameters on the enhancement of fault feature. Finally, the experimental results demonstrate that the proposed method is always valid and exhibits the superiority in diagnosis performance and operating efficiency, especially in several typical difficult cases, such as corrupted record, low signal-to-noise ratio (SNR), and non-periodic impulses.

Stochastic resonance behavior of FitzHugh–Nagumo neurons induced by electromagnetic field driven by phase noise

Noise widely exists in the nervous system, and plays an extremely important role in the information processing of the nervous system, which can enhance or weaken the ability of the nervous system to process information. Nerve cells exist in complex and changeable electromagnetic fields, and their potential changes are significantly regulated by electromagnetic induction. In response to this, first, a memristor is used to simulate the electromagnetic field environment where the nervous system is located, when using different weak periodic signals as the input of the neuron system, the rich stochastic resonance behavior of the FitzHugh–Nagumo neuron system is analyzed under the drive of phase noise. Second, taking the amplitude, period and intensity of phase noise as the main change parameters, and the changes of the parameters of the memristor and the period of the external signal as auxiliary conditions, the stochastic resonance dynamics analysis is carried out from three perspectives: the amplitude and period of phase noise, the amplitude and intensity of phase noise and the intensity and period of phase noise.

Stochastic Resonance in Organic Electronic Devices.

Stochastic Resonance (SR) is a phenomenon in which noise improves the performance of a system. With the addition of noise, a weak input signal to a nonlinear system, which may exceed its threshold, is transformed into an output signal. In the other words, noise-driven signal transfer is achieved. SR has been observed in nonlinear response systems, such as biological and artificial systems, and this review will focus mainly on examples of previous studies of mathematical models and experimental realization of SR using poly(hexylthiophene)-based organic field-effect transistors (OFETs). This phenomenon may contribute to signal processing with low energy consumption. However, the generation of SR requires a noise source. Therefore, the focus is on OFETs using materials such as organic materials with unstable electrical properties and critical elements due to unidirectional signal transmission, such as neural synapses. It has been reported that SR can be observed in OFETs by application of external noise. However, SR does not occur under conditions where the input signal exceeds the OFET threshold without external noise. Here, we present an example of a study that analyzes the behavior of SR in OFET systems and explain how SR can be made observable. At the same time, the role of internal noise in OFETs will be explained.

Emergence of stochastic resonance in a two-compartment hippocampal pyramidal neuron model.

In vitro studies have shown that hippocampal pyramidal neurons employ a mechanism similar to stochastic resonance (SR) to enhance the detection and transmission of weak stimuli generated at distal synapses. To support the experimental findings from the perspective of multicompartment model analysis, this paper aimed to elucidate the phenomenon of SR in a noisy two-compartment hippocampal pyramidal neuron model, which was a variant of the Pinsky-Rinzel neuron model with smooth activation functions and a hyperpolarization-activated cation current. With a bifurcation analysis of the model, we demonstrated the underlying dynamical structure responsible for the occurrence of SR. Furthermore, using a stochastically generated biphasic pulse train and broadband noise generated by the Orenstein-Uhlenbeck process as noise perturbation, both SR and suprathreshold SR were observed and quantified. Spectral analysis revealed that the distribution of spectral power under noise perturbations, in addition to inherent neurodynamics, is the main factor affecting SR behavior. The research results suggested that noise enhances the transmission of weak stimuli associated with elongated dendritic structures of hippocampal pyramidal neurons, thereby providing support for related laboratory findings.

Stochastic resonance in asymmetric bistable coupled network systems driven by Gaussian colored noise

In this work studied is the synergistic effect of asymmetric bistable coupled network systems under the action of Gaussian colored noise and periodic signal. The system is a network model consisting of a large number of oscillators. The interaction and change between individuals produce complex nonlinear behavior patterns. For further research, firstly, the original N-dimensional system is reduced and approximated by using the mean field theory, the unified colored noise approximation theory and the equivalent nonlinearization method. Secondly, the Langevin equation of simplified model is obtained through the slaving principle by using the two-state model theory to derive the theoretical expression of signal-to-noise ratio. It is found that the system produces the phenomenon of scale stochastic resonance. Finally, the effects of Gaussian color noise parameters, system parameters and periodic signal parameters on the stochastic resonance behavior of asymmetric coupled network systems are discussed. The results show that the increase of Gaussian colored noise correlation time and noise intensity can promote the scale stochastic resonance phenomenon; selecting appropriate coupling coefficient can achieve the optimal stochastic resonance effect. And the stochastic resonance phenomenon of the system driven by the Gaussian colored noise and the Gaussian white noise, respectively, are analyzed and compared with each other. Research result shows that Gaussian colored noise is more conducive to enhancing stochastic resonance phenomenon.

Phenomenon of double entropic stochastic resonance with recycled noise

The double entropic stochastic resonance (DSR) phenomenon for a Brown particle moving in a confined geometry driven by a time-dependent force in the declining direction subject to additive master noise and recycled noise is investigated in this paper. Under the adiabatic approximation condition, based on two-state theory and linear response theory, the expression for the system linear response (LR) is derived. Stochastic resonance (SR) and periodic SR behavior is observed when the LR changes with the feedback coefficient and with the time-delay of the recycled noise. DSR phenomenon appears when the LR varies with the constant component and with the fluctuation noise intensity of the force in the declining direction. Tradition SR occurs on the curve of the LR when the LR varies with the intensity of the master noise. The non-monotonous effect of the parameters of the confined structure on the LR is discussed.

Bearing fault diagnosis based on the active energy conversion of generalized stochastic resonance in fluctuating-frequency linear oscillator

Noise-assisted stochastic resonance (SR) method has been extensively applied in bearing fault diagnosis. In order to cast off the basic constraint on nonlinearity in classical SR systems, and overturn the passive energy conversion from external noise to signal, a fluctuating-frequency linear oscillator (FFLO) is proposed and combined with the generalized scale transformation (GST) to overcome the small parameter limitation in this study. The results of output power amplification reveal that the proposed GST-FFLO system displays a rich variety of generalized SR (GSR) behaviors, which play an active role in the optimal energy conversion from internal regulatable noise to weak bearing fault signal. Moreover, it is also found that the undamped GST-FFLO system always produces more significant GSR peaks, thereby improving the precision and efficiency in the energy conversion. Finally, the experimental results demonstrate that the proposed method is always valid and exhibits the superiority in diagnosis performance and operating efficiency in several typical difficult cases, namely, impulse interference, low signal-to-noise ratio, and multiple faults.

Resonance behavior for a trapped particle described by a three-dimensional fractional Langevin equation

The stochastic resonance (SR) behavior of a trapped particle characterized by a three-dimensional fractional-order stochastic equation with Markovian trichotomous noise has been studied in our work. Significantly, an exact expression of the first moment is derived by Shapiro-Loginov formula. Furthermore, the non-monotonic behavior of output amplitude is further discussed. Moreover, the asymptotic behaviors of relaxation function have been discussed. And the periodicity of the time series of the first moment is also addressed to verify the exact expression of the first moment in a long time. Particularly, the SR phenomenon induced by the trichotomous noise is studied. It is worthy to mention that the existence of SR in a fractional Langevin equation (FLa graphical method. Material resonance behaviors of the output amplitude versus the system parameters and noise parameters are extensively investigated. Especially, reverse SR phenomenon, stochastic multiresonance phenomena and bona fide SR are addressed in detail.

Stochastic dynamic behavior of FitzHugh–Nagumo neurons stimulated by white noise

Stochastic noise exists widely in the nervous system, and noise plays an extremely important role in the information processing of the nervous system. Noise can enhance the ability of neurons to process information as well as decrease it. For the dynamic behavior of stochastic resonance and coherent resonance shown by neurons under the action of stochastic noise, this paper uses Fourier coefficient and coherence resonance coefficient to measure the behavior of stochastic resonance and coherence resonance, respectively, and some conclusions are drawn by analyzing the effects of additive noise and multiplicative noise. Appropriate noise can make the nonlinear system exhibit stochastic resonance behavior and enhance the detection ability of external signals. It can also make the coherent resonance behavior of the nonlinear system reach its optimal state, and the system becomes more orderly. By comparing the effects of additive and multiplicative noise on the stochastic resonance behavior and coherent resonance behavior of the system, it is found that additive and multiplicative noise can both make the system appear the phenomenon of stochastic resonance and have almost identical discharge state at the same noise intensity. However, with the increase of noise intensity, the coherent resonance of the system occurs, the multiplicative noise intensity is smaller than that of additive noise, but the coherent resonance coefficient of additive noise is smaller and the coherent resonance effect is better. The system whose system parameters are located near the bifurcation point is more prone to coherent resonance, and the closer the bifurcation point is, the more obvious the coherent resonance phenomenon is, and the more regular the system becomes. When the parameters of the system are far away from the bifurcation point, the coherent resonance will hardly appear. Besides, when additive and multiplicative noise interact together, the stochastic resonance and coherent resonance phenomena are more likely to appear at small noise, and the behavior of stochastic resonance and coherent resonance that the system shown is better in the local range.

Enhanced energy harvesting using time-delayed feedback control from random rotational environment

Motivated by improving performance of a bi-stable vibration energy harvester (VEH) from the viewpoint of vibration control, the time-delayed feedback control of displacement and velocity are constructively proposed into an electromechanical coupled VEH mounted on a rotational automobile tire, which is subject to colored noise and the periodic excitation. Using the improved stochastic averaging procedure based on energy-dependent frequency, the expressions of stationary probability density (SPD) and signal-to-noise ratio (SNR) are obtained analytically. Then, the efficiency of time-delayed feedback control on the stationary response and stochastic resonance (SR) for the delay-controlled VEH is explored in detail theoretically. Results show that both noise-induced SR and delay-induced SR can occur. Time delay is able to not only enhance the SR behavior but also weaken it. Furthermore, a larger negative feedback gain of displacement and a larger positive feedback gain of velocity are more beneficial for VEH. Interesting finding is that the optimal combination of time delay in maximizing the harvested performance, such as the harvest power, the output voltage and the power conversion efficiency, is almost perfectly consistent with that in maximizing SNR. Compared with the uncontrolled VEH, the delay-controlled VEH can achieve certain desirable optimization in harvesting energy by choosing the appropriate combination of time delays and feedback gains.

Stochastic resonance induced weak signal enhancement over controllable potential-well asymmetry

A dynamical model submerged in two colored multiplicative and additive noises by colored cross-correlation is established to elaborate controllable asymmetric potential-well with depth-asymmetry and width-asymmetry. We deduce the approximate signal-to-noise ratio (SNR) as widely adopted indicator for quantifying stochastic resonance (SR) behavior in accordance with the two-state theory, where the largest SNR peaks are almost attained in the asymmetry case. Moreover, the non-monotonic resonance curves excited by the incremental multiplicative colored noise intensity show the typical SR phenomenon and the SNR peaks decline as the additive colored noise intensity increases, the SR behavior induced by multiplicative colored noise is different from that induced by varying additive one. Noteworthy, the self-correlation time of alternative noises are more effective for controlling SR than cross-correlation time of noises. More interestingly, the output SNR demonstrates double resonance peaks by varying the cross-correlation intensity from negative to positive, however, the two local optimal cross-correlation intensities are almost maintained constant as the increasing of additive noise intensity. Even the large asymmetric well-depth is always beneficial to the improvement of SNR in comparison with well-width asymmetry at the same situation, which is due to the much more energy harvesting from the noises.

Stochastic resonance in synapse-mimicking ferroelectric organic field-effect transistor

Ferroelectric organic field-effect transistors (FE-OFETs) are fabricated to implement the functions of a neural synapse, including one-directional signal transmission and synaptic plasticity. Stochastic resonance (SR) experiments are conducted with FE-OFETs that use regioregular poly(3-hexylthiophene-2,5-diyl) as the semiconductor layer and poly(vinylidene fluoride-co-hexafluoropropylene) as the insulator layer. The input–output correlation is observed to increase as the external noise intensity rises, with a cutoff frequency of 1 Hz, demonstrating the experimental occurrence of SR in the fabricated FE-OFETs. Furthermore, vibrational resonance experiments are performed to clarify the frequency-dependence of the SR behavior. The peak input–output correlation shifts toward higher amplitudes of a secondary sine wave that is applied instead of external noise as the frequency of the input signal rises from = 0.5–1 Hz. The FE-OFETs exhibit more adaptive behavior than paraelectric OFETs, with a threshold voltage that changes dynamically according to the frequency characteristics of the input signal and/or external noise. Furthermore,the immediate response to abrupt environmental changes via the SR phenomenon and flexible behavior based on past experience via hysteresis effects can be implemented by a single FE-OFET element.

Collective stochastic resonance behaviors of two coupled harmonic oscillators driven by dichotomous fluctuating frequency* *Project supported by the National Natural Science Foundation of China for the Youth (Grant Nos. 11501385 and 11801385).

The collective behaviors of two coupled harmonic oscillators with dichotomous fluctuating frequency are investigated, including stability, synchronization, and stochastic resonance (SR). First, the synchronization condition of the system is obtained. When this condition is satisfied, the mean-field behavior is consistent with any single particle behavior in the system. On this basis, the stability condition and the exact steady-state solution of the system are derived. Comparative analysis shows that, the stability condition is stronger than the synchronization condition, that is to say, when the stability condition is satisfied, the system is both synchronous and stable. Simulation analysis indicates that increasing the coupling strength will reduce the synchronization time. In weak coupling region, there is an optimal coupling strength that maximizes the output amplitude gain (OAG), thus the coupling-induced SR behavior occurs. In strong coupling region, the two particles are bounded as a whole, so that the coupling effect gradually disappears.