Multiple Stochastic Resonances 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.

Multiple stochastic resonances and inverse stochastic resonances in asymmetric bistable system under the ultra-high frequency excitation

Multiple stochastic resonances and inverse stochastic resonances in asymmetric bistable system under the ultra-high frequency excitation

Inverse stochastic resonance in modular neural network with synaptic plasticity

This work explores the inverse stochastic resonance (ISR) induced by bounded noise and the multiple inverse stochastic resonance induced by time delay by constructing a modular neural network, where the modified Oja’s synaptic learning rule is employed to characterize synaptic plasticity in this network. Meanwhile, the effects of synaptic plasticity on the ISR dynamics are investigated. Through numerical simulations, it is found that the mean firing rate curve under the influence of bounded noise has an inverted bell-like shape, which implies the appearance of ISR. Moreover, synaptic plasticity with smaller learning rate strengthens this ISR phenomenon, while synaptic plasticity with larger learning rate weakens or even destroys it. On the other hand, the mean firing rate curve under the influence of time delay is found to exhibit a decaying oscillatory process, which represents the emergence of multiple ISR. However, the multiple ISR phenomenon gradually weakens until it disappears with increasing noise amplitude. On the same time, synaptic plasticity with smaller learning rate also weakens this multiple ISR phenomenon, while synaptic plasticity with larger learning rate strengthens it. Furthermore, we find that changes of synaptic learning rate can induce the emergence of ISR phenomenon. We hope these obtained results would provide new insights into the study of ISR in neuroscience.

Non-Gaussian noise and autapse-induced inverse stochastic resonance in bistable Izhikevich neural system under electromagnetic induction

Inverse stochastic resonance refers to the phenomenon that the average firing rate of a neuron is inhibited by noise, of which mechanism is widely used in a variety of biological cells and economic phenomena. In this paper, a bistable Izhikevich neural model and triple-neuron feed-forward loop Izhikevich neural network motifs under the effects of electromagnetic induction are constructed to investigate the phenomenon of inverse stochastic resonance induced by Non-Gaussian colored noise and electrical autapse. It is found that there exists a minimum value of the average firing rate curve caused by intensity of non-Gaussian colored noise, which is the phenomenon of inverse stochastic resonance. Obtained results also show that the inverse stochastic resonance induced by electrical autapse shows a decaying oscillation process with respect to synaptic delay time, and further research indicates that average firing rate has several minimums as a function of time delay of electrical autapse, which is called multiple inverse stochastic resonance. Furthermore, the inverse stochastic resonance in triple-neuron feed-forward loop Izhikevich neural network motifs are also examined, and it is confirmed that the responses of single Izhikevich neuron and neural network motifs to different parameters show consistency under same conditions, but also show some differences. Finally, the effects of electromagnetic induction on inverse stochastic resonance are checked both in single Izhikevich neural model and feed-forward loop network motifs. Electromagnetic induction feedback gain coefficient k1 should not be too large under certain conditions, otherwise it may cause FFL network motifs to loss the function of suppressing the discharge activity. No matter how the values of electromagnetic induction parameter k2 and magnetic flux leakage coefficient k3 change, they basically cannot affect the ISR in the feed-forward loop neural network motifs The conclusions of this paper may help researchers understanding how using unique mechanism of inverse stochastic resonance to find advantages and avoid disadvantages in biomedical field and many interdisciplinary research.

Effects of bounded noise and time delay on signal transmission in excitable neural networks

The influence of bounded noise and time delay on the sub–threshold signal transmission in FitzHugh–Nagumo neuronal networks is studied in this paper. It is found that the signal transmission performance can be enhanced by moderate noise levels in neuronal systems. There is an optimal cross–correlation time where the noise enhances signal transmission best. Moreover, the positively correlated bounded noise–induced stochastic anti–resonance phenomenon monotonically enhances with the increasing cross–correlated intensity. Interestingly, the stochastic anti–resonance phenomenon disappears when the noise is negatively correlated. With the fine–tuning of the time delay, the resonance peaks occur at each half–integer multiples of the signal period, implying delay–induced multiple stochastic resonances. The sub–harmonic stochastic resonance and stochastic anti–resonance alternatively appear at the appropriate coupling strength. These results may provide a novel perspective on sub–threshold signal transmission in the nervous system.

Autapse-induced multiple inverse stochastic resonance in a neural system

We mainly investigate the multiple inverse stochastic resonance (ISR) induced by electrical autapse and chemical autapse under different types of input current. It is found that average firing rate is shown as a decaying oscillation process with time delay for both electrical autapse and chemical autapse under noise and input current. Furthermore, we find that average firing rate has several minimums as a function of time delay of autapse, which is called multiple ISR. As a consequence, our work suggests that, autapse can regulate and control the neuronal activities and induce multiple ISR. Compared with signal current, the multiple ISR phenomenon driven by constant current is more apparent.

Stochastic multiresonance in oscillators induced by bounded noise

Stochastic resonance (SR) in a harmonic oscillator with parametric bounded noise and external periodic force is investigated. By applying the property of bounded noise and using Cameron–Martin formula, infinite chains of linear differential equations are obtained for the spectral amplification, mean-square displacement, and variance. Multiple stochastic resonances are observed for these characteristics. Relationships with resonant tongues of the Mathieu equation are established. It is shown that similar effects can be observed in the case of harmonic noise external force. The case of two coupled oscillators is also studied. Analysis is based on a natural truncation of the infinite moment chains and using of the numerical matrix computations.

A Spectrum Sensing Technology Exploiting Multiple Large Eigenvalues and Stochastic Resonance

Cognitive radio (CR) is a hopeful technology to reduce the negative effect of spectrum scarcity caused by the enormous amount of wireless mobile device. Spectrum sensing could alleviate the interference and harm for primary user, and enhance the wireless access capability. This paper proposes a novel spectrum sensing method by using the summation of multiple large eigenvalues (SMLE) and stochastic resonance (SR). SR is used to enforce the detection signal of multiple antennas in low SNR condition. Then the sample covariance matrix of the enforcing detection signals and its multiple large eigenvalues are computed for constructing test statistic. The simulation results demonstrate that the proposed detector based on SMLE and SR is superior than the existing detector based on SMLE, and is robust in strong noise background.

Multiple Stochastic Resonances and Oscillation Transitions in Cortical Networks With Time Delay

Stochasticity and oscillation play a vital role in neural signal processing. Time delay, which is inevitable in biological neural systems, has significant effect on the dynamics of neuronal networks. This paper provides an analysis of how time delay affects stochastic resonance and firing rate oscillation of cortical neuronal networks. A cortical network is established and mean-field theory is applied to analytically compute the dynamical response of networks. When the frequency of external stimulation is close to intrinsic frequency of neuronal networks, firing rate exhibits coherent oscillation and the phenomenon of stochastic resonance occurs in inhibitory neurons. Time delay can induce multiple stochastic resonances, which appear intermittently at integer multiples of the period of input signal, due to the transition of network dynamics induced by time delays. The fluctuation of membrane potential and instantaneous firing rate of cortical networks achieve maximal periodically with the variation of time delay. Furthermore, time delay and electrical coupling play complementary roles in determining network responses. Network oscillation can transit from unstable to stable when coupling strength exceeds a critical value. Transition threshold is lower for time delays close to integer multiples of input period where resonant response of cortical network enhances the formation of stable oscillation.

How electromagnetic induction and coupled delay affect stochastic resonance in a modified neuronal network subject to phase noise

Through introducing the ingredients of electromagnetic induction and coupled time delay into the original Fitzhugh–Nagumo (FHN) neuronal network, the dynamics of stochastic resonance in a model of modified FHN neuronal network in the environment of phase noise is explored by numerical simulations in this study. On one hand, we demonstrate that the phenomenon of stochastic resonance can appear when the intensity of phase noise is appropriately adjusted, which is further verified to be robust to the edge-added probability of small-world network. Moreover, under the influence of electromagnetic induction, the phase noise-induced resonance response is suppressed, meanwhile, a large noise intensity is required to induce stochastic resonance as the feedback gain of induced current increases. On the other hand, when the coupled time delay is incorporated into this model, the results indicate that the properly tuned time delay can induce multiple stochastic resonances in this neuronal network. However, the phenomenon of multiple stochastic resonances is found to be restrained upon increasing feedback gain of induced current. Surprisingly, by changing the period of phase noise, multiple stochastic resonances can still emerge when the coupled time delay is appropriately tuned to be integer multiples of the period of phase noise.

Stochastic resonance of drawdown risk in energy market prices

We investigate the stochastic resonance dynamic behavior characteristics of price drawdown time series driven by internal and external periodic information and discuss the influence of information resonance on price drawdown risk, based on price drawdown, periodic Heston model and signal power amplification. A theoretical model of the periodic price drawdown time series is proposed to describe the energy price drawdown time series with the periodic Heston model. Then the signal power amplification (SPA) is employed to measure the stochastic resonance phenomenon in the internal and external periodic information environment of complex energy dynamics system. Combined with the real data of WTI spot price of NYMEX, the least square method of drawdown time series distribution is used to estimate the parameters of the model. The probability density functions of drawdown between the theoretical model and the real data are compared, and a good agreement can be found between both the simulated data from the proposed model and the real data. After the stochastic simulation of signal power amplification under internal and external periodic information respectively, the results show that: (i) In the functions of SPA versus price volatility parameters (noise correlation strength or periodic information strength), inverse resonance phenomenon can be observed, that is to say, there is the best system price volatility parameter, noise correlation strength and information strength corresponding to the least risk of the price drawdown; (ii) In the SPA versus amplitude of volatility fluctuations, the correlation induce multiple inverse stochastic resonance phenomenon can be observed; (iii) The increase of growth rate strengthens SPA and weakens drawdown risk of energy market prices.

Firing Rate Oscillation and Stochastic Resonance in Cortical Networks With Electrical–Chemical Synapses and Time Delay

The stochastic dynamics of neural network are studied and the phenomenon of stochastic resonance is found in inhibitory neurons, whose firing rate is close to the frequency of external stimulation. Time delay in the neural coupling process can induce multiple stochastic resonances, which appear intermittently at the integer multiples of the oscillation period of the input signal. It is found that the time delay can induce the periodic oscillation of neural firing rate, which may account for the occurrence of multiple stochastic resonances. In addition, the effect of synapses on firing rate oscillation and network resonance is investigated. As the strength of gap-junction and inhibitory-inhibitory chemical coupling is increased, the maximal resonant value increases, while the resonant frequency is unchanged. However, the resonant frequency and peak value increase with the coupling strength of excitatory–inhibitory chemical synapses. This difference may result from the interaction of excitation and inhibition within the cortical network. We further apply mean-field theory to time-delayed network model to validate the obtained numerical results. Both time delay and electrical–chemical synapses play an important role in firing rate oscillation and stochastic resonance within the cortical network, determining the ability to enhance the transmission of information in neural systems.

Combined effects of time delay and noise on the ability of neuronal network to detect the subthreshold signal

Recently, we found that there exist several optimal noise intensities at which the subthreshold signal could be detected efficiently in small-world neuronal networks. And this phenomenon is called as multiple stochastic resonance. Based on our former obtained results, we investigate combined effects of time delay and noise on the ability of such small-world neuronal networks to detect subthreshold signal furthermore. With the numerical simulation results, we reveal three important information. Firstly, when noise intensity takes optimal values, the ability of neuronal network to detect the subthreshold signal could be either maintained at high level as delay-free case or decreased by time delay; secondly, when noise intensity is not optimal in the absence of time delay, time delay could also assist noise to detect the subthreshold signal; finally, when noise intensity reaches a certain level, the detecting ability of the neuronal network could be optimized not only at multiples of the period of the subthreshold signal but also at some small values of time delay.

Stochastic resonance in FitzHugh–Nagumo neural system driven by correlated non-Gaussian noise and Gaussian noise

In this paper, the phenomenon of stochastic resonance in FitzHugh–Nagumo (FHN) neural system driven by correlated non-Gaussian noise and Gaussian white noise is investigated. First, the analytical expression of the stationary probability distribution is derived by using the path integral approach and the unified colored noise approximation. Then, we obtain the expression of signal-to-noise ratio (SNR) by applying the theory of two-state model. The results show that the phenomena of stochastic resonance and multiple stochastic resonance appear in FHN neural system under different values of parameters. The effects of the multiplicative noise intensity D and the additive noise intensity Q on the SNR are entirely different. In addition, the discharge behavior of FHN neural system is restrained when the value of Q is smaller. But, it is conducive to enhance signal response of FHN neural system when the values of Q and D are relatively larger.

Autapse-induced multiple stochastic resonances in a modular neuronal network.

This study investigates the nontrivial effects of autapse on stochastic resonance in a modular neuronal network subjected to bounded noise. The resonance effect of autapse is detected by imposing a self-feedback loop with autaptic strength and autaptic time delay to each constituent neuron. Numerical simulations have demonstrated that bounded noise with the proper level of amplitude can induce stochastic resonance; moreover, the noise induced resonance dynamics can be significantly shaped by the autapse. In detail, for a specific range of autaptic strength, multiple stochastic resonances can be induced when the autaptic time delays are appropriately adjusted. These appropriately adjusted delays are detected to nearly approach integer multiples of the period of the external weak signal when the autaptic strength is very near zero; otherwise, they do not match the period of the external weak signal when the autaptic strength is slightly greater than zero. Surprisingly, in both cases, the differences between arbitrary two adjacent adjusted autaptic delays are always approximately equal to the period of the weak signal. The phenomenon of autaptic delay induced multiple stochastic resonances is further confirmed to be robust against the period of the external weak signal and the intramodule probability of subnetwork. These findings could have important implications for weak signal detection and information propagation in realistic neural systems.

Adaptive stochastic resonance in self-organized small-world neuronal networks with time delay

In this paper, adaptive stochastic resonance in time-delayed Newman–Watts small-world neuronal networks is studied, where the strength of synaptic connections between neurons is adaptively modulated by spike-timing-dependent plasticity (STDP). Numerical results show that, in the absence of information transmission delay, the phenomenon of stochastic resonance occurs and the efficiency of networked stochastic resonance can be slightly depressed by STDP. Due to the reduction of strong couplings induced by STDP, for a larger adjusting rate of STDP, a smaller peak value of the resonance response is obtained. In addition, the effect of stochastic resonance can be either promoted or destroyed by time delay, and multiple stochastic resonances appear intermittently at the integer multiples of periods of the subthreshold forcing. Furthermore, it is demonstrated that the networked stochastic resonance can also be dramatically affected by the small-world topology. For small and moderate adjusting rate of STDP, fine-tuning of the probability of adding links can significantly enhance the effect of stochastic resonance in adaptive neural network. Additionally, there is an optimal probability of adding links by which the noise-induced transmission of weak periodic signal peaks and the location of this span depends largely on the time delay and adjusting rate.

Effects of time delay and random rewiring on the stochastic resonance in excitable small-world neuronal networks

The effects of time delay and rewiring probability on stochastic resonance and spatiotemporal order in small-world neuronal networks are studied in this paper. Numerical results show that, irrespective of the pacemaker introduced to one single neuron or all neurons of the network, the phenomenon of stochastic resonance occurs. The time delay in the coupling process can either enhance or destroy stochastic resonance on small-world neuronal networks. In particular, appropriately tuned delays can induce multiple stochastic resonances, which appear intermittently at integer multiples of the oscillation period of the pacemaker. More importantly, it is found that the small-world topology can significantly affect the stochastic resonance on excitable neuronal networks. For small time delays, increasing the rewiring probability can largely enhance the efficiency of pacemaker-driven stochastic resonance. We argue that the time delay and the rewiring probability both play a key role in determining the ability of the small-world neuronal network to improve the noise-induced outreach of the localized subthreshold pacemaker.

Effects of time delay on the stochastic resonance in small-world neuronal networks

The effects of time delay on stochastic resonance in small-world neuronal networks are investigated. Without delay, an intermediate intensity of additive noise is able to optimize the temporal response of the neural system to the subthreshold periodic signal imposed on all neurons constituting the network. The time delay in the coupling process can either enhance or destroy stochastic resonance of neuronal activity in the small-world network. In particular, appropriately tuned delays can induce multiple stochastic resonances, which appear intermittently at integer multiples of the oscillation period of weak external forcing. It is found that the delay-induced multiple stochastic resonances are most efficient when the forcing frequency is close to the global-resonance frequency of each individual neuron. Furthermore, the impact of time delay on stochastic resonance is largely independent of the small-world topology, except for resonance peaks. Considering that information transmission delays are inevitable in intra- and inter-neuronal communication, the presented results could have important implications for the weak signal detection and information propagation in neural systems.

Effect of the heterogeneous neuron and information transmission delay on stochastic resonance of neuronal networks

We study the effect of heterogeneous neuron and information transmission delay on stochastic resonance of scale-free neuronal networks. For this purpose, we introduce the heterogeneity to the specified neuron with the highest degree. It is shown that in the absence of delay, an intermediate noise level can optimally assist spike firings of collective neurons so as to achieve stochastic resonance on scale-free neuronal networks for small and intermediate α(h), which plays a heterogeneous role. Maxima of stochastic resonance measure are enhanced as α(h) increases, which implies that the heterogeneity can improve stochastic resonance. However, as α(h) is beyond a certain large value, no obvious stochastic resonance can be observed. If the information transmission delay is introduced to neuronal networks, stochastic resonance is dramatically affected. In particular, the tuned information transmission delay can induce multiple stochastic resonance, which can be manifested as well-expressed maximum in the measure for stochastic resonance, appearing every multiple of one half of the subthreshold stimulus period. Furthermore, we can observe that stochastic resonance at odd multiple of one half of the subthreshold stimulus period is subharmonic, as opposed to the case of even multiple of one half of the subthreshold stimulus period. More interestingly, multiple stochastic resonance can also be improved by the suitable heterogeneous neuron. Presented results can provide good insights into the understanding of the heterogeneous neuron and information transmission delay on realistic neuronal networks.

Delay-induced multiple stochastic resonances on scale-free neuronal networks

We study the effects of periodic subthreshold pacemaker activity and time-delayed coupling on stochastic resonance over scale-free neuronal networks. As the two extreme options, we introduce the pacemaker, respectively, to the neuron with the highest degree and to one of the neurons with the lowest degree within the network, but we also consider the case when all neurons are exposed to the periodic forcing. In the absence of delay, we show that an intermediate intensity of noise is able to optimally assist the pacemaker in imposing its rhythm on the whole ensemble, irrespective to its placing, thus providing evidences for stochastic resonance on the scale-free neuronal networks. Interestingly thereby, if the forcing in form of a periodic pulse train is introduced to all neurons forming the network, the stochastic resonance decreases as compared to the case when only a single neuron is paced. Moreover, we show that finite delays in coupling can significantly affect the stochastic resonance on scale-free neuronal networks. In particular, appropriately tuned delays can induce multiple stochastic resonances independently of the placing of the pacemaker, but they can also altogether destroy stochastic resonance. Delay-induced multiple stochastic resonances manifest as well-expressed maxima of the correlation measure, appearing at every multiple of the pacemaker period. We argue that fine-tuned delays and locally active pacemakers are vital for assuring optimal conditions for stochastic resonance on complex neuronal networks.