Phenomenon Of Coherence Resonance Research Articles

Forecasting coherence resonance in a stochastic Fitzhugh–Nagumo neuron model using reservoir computing

We delve into the intriguing realm of reservoir computing to predict the intricate dynamics of a stochastic FitzHugh–Nagumo neuron model subjected to external noise. Through innovative reservoir design and training, we unveil the remarkable capacity of a reservoir computer to forecast the behavior of this stochastic system across a wide spectrum of noise intensity variations. Notably, our reservoir computer astutely replicates the intricate phenomenon of coherence resonance in the stochastic FitzHugh–Nagumo neuron, signifying the superior modeling capabilities of this approach. A detailed examination of the microscopic dynamics within the reservoir’s hidden layer reveals the emergence of distinct neuronal clusters, each displaying unique behaviors. Certain neurons within the reservoir are adept at faithfully reproducing the dynamical traits of the neuron, particularly the spike generation mechanism. In contrast, the remaining neurons within the reservoir seem to emulate stochastic influences with remarkable precision, accurately capturing the moments of spike generation in the neuron under the sway of noise. This innovative reservoir design proves to be highly effective across a diverse range of noise control parameters, faithfully replicating the essential characteristics of the original stochastic FitzHugh–Nagumo neuron. These findings illuminate the potential of reservoir computing to model and predict the dynamics of complex stochastic systems, showcasing its adaptability and versatility in understanding and simulating natural phenomena.

How random fluctuations can generate and suppress complex oscillatory regimes in continuous stirred tank reactors

Motivated by important chemical engineering applications, we study probabilistic mechanisms of stochastic effects in a randomly forced model of the continuous stirred tank reactor. The bifurcation analysis of the deterministic model reveals the parameter zone of bistability with coexistence of the equilibrium and oscillatory regimes. It is shown that the boundary between basins of these regimes is moving as the bifurcation parameter changes. We study noise-induced transitions across this boundary leading to the stochastic generation of spiking oscillations and backward effect of the noise-induced suppression of large-amplitude spiking. In the study of these stochastic effects, we use statistics extracted from the direct numerical simulation, and an analytical approach using confidence ellipses method. An important probabilistic phenomenon of coherence resonance is revealed and discussed.

Tuning magneto-electric coherent resonance with a deep-subwavelength localized spoof surface plasmonic structure.

It has been recently shown that an ultrathin corrugated spiral metal strip can simultaneously support electric and magnetic localized spoof plasmonic modes at lower frequencies. In this Letter, we report a mirror quasi-symmetrical corrugated spiral metal disk which can support coherent resonance of an orthogonal electric dipole and a magnetic dipole to achieve azimuthally symmetric unidirectional scattering. By tuning the geometric dimensions, reconfigurable magneto-electric (ME) coherent resonance enhancement is realized. Excellent agreement between numerical simulations and experimental results verifies the tunable ME coherent resonance phenomenon. Our finding could anticipate future sensitive and versatile functional devices based on high-Q coherent resonance from the microwave to the terahertz bands.

How noise can generate calcium spike-type oscillations in deterministic equilibrium modes.

Stochastic excitability of spiking oscillatory regimes in the calcium kinetics is studied on the basis of the Li-Rinzel conceptual model. The probabilistic mechanisms of the noise-induced generation of large-amplitude oscillations in parametric zones, where the original deterministic model has only stable equilibria, are investigated numerically and analytically. A parametric statistical description of interspike intervals is curried out and the phenomenon of coherence resonance is discussed. For the analytical study of the stochastic excitement, the confidence domain method using a stochastic sensitivity technique is applied. In this analysis, a key role of mutual arrangement of the confidence ellipses and separatrices detaching the sub- and supercritical regions is demonstrated. It is shown that in the Li-Rinzel model such separatrices are the stable manifolds of the saddle equilibria and the transient semiattractors.

Interlayer Connectivity Affects the Coherence Resonance and Population Activity Patterns in Two-Layered Networks of Excitatory and Inhibitory Neurons.

The firing patterns of neuronal populations often exhibit emergent collective oscillations, which can display substantial regularity even though the dynamics of individual elements is very stochastic. One of the many phenomena that is often studied in this context is coherence resonance, where additional noise leads to improved regularity of spiking activity in neurons. In this work, we investigate how the coherence resonance phenomenon manifests itself in populations of excitatory and inhibitory neurons. In our simulations, we use the coupled FitzHugh-Nagumo oscillators in the excitable regime and in the presence of neuronal noise. Formally, our model is based on the concept of a two-layered network, where one layer contains inhibitory neurons, the other excitatory neurons, and the interlayer connections represent heterotypic interactions. The neuronal activity is simulated in realistic coupling schemes in which neurons within each layer are connected with undirected connections, whereas neurons of different types are connected with directed interlayer connections. In this setting, we investigate how different neurophysiological determinants affect the coherence resonance. Specifically, we focus on the proportion of inhibitory neurons, the proportion of excitatory interlayer axons, and the architecture of interlayer connections between inhibitory and excitatory neurons. Our results reveal that the regularity of simulated neural activity can be increased by a stronger damping of the excitatory layer. This can be accomplished with a higher proportion of inhibitory neurons, a higher fraction of inhibitory interlayer axons, a stronger coupling between inhibitory axons, or by a heterogeneous configuration of interlayer connections. Our approach of modeling multilayered neuronal networks in combination with stochastic dynamics offers a novel perspective on how the neural architecture can affect neural information processing and provide possible applications in designing networks of artificial neural circuits to optimize their function via noise-induced phenomena.

Deterministic coherence resonance analysis of coupled chaotic oscillators: fractional approach

Recently, the stabilization of chaos by chaos has attracted the attention of researchers. A small deviation between the natural frequencies of unidirectionally coupled chaotic oscillators can cause the emerge of a coherence resonance in the slave oscillator for a given coupling strength. In this work, we investigate the phenomenon of coherence resonance for a coupled Rössler system under the influence of fractional operators in the frequency response of the slave oscillator. Based on the analysis of the fractional Rössler system, we determine a range of fractional orders in which the system retains its instability, and an analysis of the frequency response of the system to changes in natural frequency is developed. Finally, the frequency response of the slave system to changes in the fractional derivative order, the natural frequency of the master system, and the coupling strength is analyzed, and how these changes promote the occurrence of coherence resonance is examined.

Capital Demand Driven Business Cycles: Mechanism and Effects

We develop a tractable macroeconomic model that captures dynamic behaviors across multiple timescales, including business cycles. The model is anchored in a dynamic capital demand framework reflecting an interactions-based process whereby firms determine capital needs and make investment decisions at the micro level. We derive equations for aggregate demand from this micro setting and embed them in the Solow growth economy. As a result, we obtain a closed-form dynamical system with which we study economic fluctuations and their impact on long-term growth. For realistic parameters, the model has two attracting equilibria: one at which the economy contracts and one at which it expands. This bi-stable configuration gives rise to quasiperiodic fluctuations, characterized by the economy's prolonged entrapment in either a contraction or expansion mode punctuated by rapid alternations between them. We identify the underlying endogenous mechanism as a coherence resonance phenomenon. In addition, the model admits a stochastic limit cycle likewise capable of generating quasiperiodic fluctuations; however, we show that these fluctuations cannot be realized as they induce unrealistic growth dynamics. We further find that while the fluctuations powered by coherence resonance can cause substantial excursions from the equilibrium growth path, such deviations vanish in the long run as supply and demand converge.

Stochastic generation and suppression of early afterdepolarizations in a three‐dimensional model of cardiac action potential

The influence of random disturbances on a three‐dimensional simplification of Luo–Rudy model of the cardiac action potential is studied. We show that in the parameter region, where the deterministic model is in the equilibrium regime, noise can trigger large‐amplitude oscillations that correspond with pathological early afterdepolarizations (EADs). For this stochastic excitement, the phenomenon of coherence resonance was discovered. On the contrary, in another parameter zone of the model, noise can suppress EADs. We analyze these stochastic phenomena using the stochastic sensitivity functions technique, Mahalanobis distance, the methods of principal directions, and confidence domains.

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.

Coherence resonance in neuronal populations: Mean-field versus network model.

The counterintuitive phenomenon of coherence resonance describes a nonmonotonic behavior of the regularity of noise-induced oscillations in the excitable regime, leading to an optimal response in terms of regularity of the excited oscillations for an intermediate noise intensity. We study this phenomenon in populations of FitzHugh-Nagumo (FHN) neurons with different coupling architectures. For networks of FHN systems in an excitable regime, coherence resonance has been previously analyzed numerically. Here we focus on an analytical approach studying the mean-field limits of the globally and locally coupled populations. The mean-field limit refers to an averaged behavior of a complex network as the number of elements goes to infinity. We apply the mean-field approach to the globally coupled FHN network. Further, we derive a mean-field limit approximating the locally coupled FHN network with low noise intensities. We study the effects of the coupling strength and noise intensity on coherence resonance for both the network and the mean-field models. We compare the results of the mean-field and network frameworks and find good agreement in the globally coupled case, where the correspondence between the two approaches is sufficiently good to capture the emergence of coherence resonance, as well as of anticoherence resonance.

The probability density function of interspike intervals in an FHN model with α-stable noise

In this paper, we expand the paradigmatic Fitzhugh–Nagumo (FHN) model by including α-stable noise and study the firing rate and coherence resonance via probability density function (PDF) of the interspike intervals (ISIs). In the previous work, different indicators and measurements are given to illustrate the firing rate and coherence resonance. However, we find that they can be described simply by the PDF of ISIs, which contains the underlying information of spiking neuron signals. For example, the width of the peak of the PDF of ISIs can characterize the phenomenon of coherence resonance. The narrower width of peak stands for the better coherence resonance.

An endogenous mechanism of business cycles

This paper suggests that business cycles may be a manifestation of coupled real economy and stock market dynamics and describes a mechanism that can generate economic fluctuations consistent with observed business cycles. To this end, we seek to incorporate into the macroeconomic framework a dynamic stock market model based on opinion interactions (Gusev et al., 2015). We derive this model from microfoundations, provide its empirical verification, demonstrate that it contains the efficient market as a particular regime and establish a link through which macroeconomic models can be attached for the study of real economy and stock market interaction. To examine key effects, we link it with a simple macroeconomic model (Blanchard, 1981). The coupled system generates nontrivial endogenous dynamics, which exhibit deterministic and stochastic features, producing quasiperiodic fluctuations (business cycles). We also inspect this system’s behavior in the phase space. The real economy and the stock market coevolve dynamically along the path governed by a stochastically-forced dynamical system with two stable equilibria, one where the economy expands and the other where it contracts, resulting in business cycles identified as the coherence resonance phenomenon. Thus, the incorporation of stock market dynamics into the macroeconomic framework, as presented here, allows the derivation of realistic behaviors in a tractable setting.

Noise-induced complex oscillatory dynamics in the Zeldovich–Semenov model of a continuous stirred tank reactor

Noise-induced variability of thermochemical processes in a continuous stirred tank reactor is studied on the basis of the Zeldovich-Semenov dynamical model. For the deterministic variant of this model, mono- and bistability parametric zones as well as local and global bifurcations are determined. Noise-induced transitions between coexisting attractors (equilibria and cycles) and stochastic excitement with spike oscillations are investigated by direct numerical simulation and the analytical approach based on the stochastic sensitivity technique. For the stochastic model, the phenomenon of coherence resonance is discovered and studied.

Capital Demand Driven Business Cycles: Mechanism and Effects

We develop a tractable macroeconomic model that captures dynamic behaviors across multiple timescales, including business cycles. The model is anchored in a dynamic capital demand framework reflecting an interactions-based process whereby firms determine capital needs and make investment decisions at the micro level. We derive equations for aggregate demand from this micro setting and embed them in the Solow growth economy. As a result, we obtain a closed-form dynamical system with which we study economic fluctuations and their impact on long-term growth. For realistic parameters, the model has two attracting equilibria: one at which the economy contracts and one at which it expands. This bi-stable configuration gives rise to quasiperiodic fluctuations, characterized by the economy's prolonged entrapment in either a contraction or expansion mode punctuated by rapid alternations between them. We identify the underlying endogenous mechanism as a coherence resonance phenomenon. In addition, the model admits a stochastic limit cycle likewise capable of generating quasiperiodic fluctuations; however, we show that these fluctuations cannot be realized as they induce unrealistic growth dynamics. We further find that while the fluctuations powered by coherence resonance can cause substantial excursions from the equilibrium growth path, such deviations vanish in the long run as supply and demand converge.

Mixed-mode self-oscillations, stochastic excitability, and coherence resonance in flows of highly concentrated suspensions

Complex mixed-mode oscillatory regimes in flows of concentrated suspensions are studied on the base of the nonlinear dynamical model. A mechanism of the generation of such regimes is associated with the N-shaped flow curve which reflects the dependence of the shear rate on the shear stress. In the zone of the unstable equilibria, amplitude and frequency characteristics of mixed-mode self-sustained oscillations are investigated. A transformation of quasi-harmonic oscillations to non-harmonic ones under increase of the stiffness of the flow curve is discussed. In the zone of the stable equilibria, a phenomenon of stochastic excitement of spike oscillations is studied by the analytical stochastic sensitivity method along with direct numerical simulations. For these mixed-mode stochastic oscillations, a parametric analysis of statistics of interspike intervals is carried out and a phenomenon of coherence resonance is discussed.

Coherence resonance-like and efficiency of financial market

We study the coherent resonance phenomenon of stock market returns and volatility and discuss the effectiveness of financial market based on the coherent resonance theory of statistical physics. In this paper, we use the Heston model to give the series describing the return and volatility. Considering the limited data of CSI 300 index, the Bayesian estimation parameters of the proposed model are given by combining Bayesian parameter estimation and realized volatility. The characteristic correlation time (CCT) and normalized fluctuations of pulse durations Rp are employed to further explore the coherent resonance behavior of stock market price returns and volatility. Based on the stochastic simulation of the estimated parameters, we can observe the phenomena of coherent resonance-like and anti-coherent resonance in CCT and Rp as a function of long-run variance and amplitude of volatility. We can also observe the critical phenomenon, there is a critical mean reversion of volatility. On both sides of the critical value, the opposite characteristics of coherent and anti-coherent resonance can be observed. The enhanced long-run variance of volatility and weakened amplitude of volatility both cause coherent-like resonance in CCT and Rp vs. the mean reversion of volatility. In addition, it can be seen that the market efficiency is lower when coherent resonance occurs, and higher when anti-coherence resonance occurs.

Coherence resonance of the spiking regularity in a neuron under electromagnetic radiation

The electrical activities are investigated in an improved Hindmarsh–Rose (HR) model with the external electromagnetic radiation of Gaussian noise. The mode transitions of the electrical activities induced by Gaussian noise are presented, such as from the rest states to the spiking states and from the spiking states to the spiking states with more or less spikes. Then, the stationary probability distribution functions of the membrane potential of the neuronal spiking are studied to explore the effect of Gaussian noise on the strength of the spiking of the neuron for the different modes of the electrical activities. In addition, the coherence of the spiking regularity of the electrical activities is investigated. The two-dimensional and three-dimensional inverse of the normalized coefficient of the variation of the spiking regularity in the improved HR with external electromagnetic radiation as Gaussian noise and external forcing current are analyzed. Then, the coherence resonance phenomenon induced by the Gaussian noise and external forcing current is discussed under three different modes of the electrical activities. The excitable effect of Gaussian noise and external forcing current on the spiking regularity of the electrical activities is explored. It is found that Gaussian noise can induce the mode transitions of the different electrical activities of the HR neuron and improve the strength of the spiking of the neuron. Gaussian noise and external forcing current can both optimally promote the spiking regularity of the different electrical activities of the neuron.

Bounded noise-induced coherence resonance in a single Rulkov neuron

Based on the chaotic Rulkov model, we investigate the impacts of bounded noise on firing activity of the neural system. First, the chaotic neural model and bounded noise are introduced and analyzed. Then, different firing patterns of the neural model driven by bounded noise are present. Finally, taking the coherence parameter R to measure the regularity of firing behavior, it is demonstrated that the regularity of neural membrane potential could achieve optimal by adjusting either the intensity of bounded noise or its frequency to an appropriate value, which means that the phenomenon of coherence resonance occurs. Moreover, it is found that coherence resonance can also be induced by another kind of bounded noise, called sine-Wiener noise. The results of this paper are beneficial to explore the functional role of noise on neural system.

An Endogenous Mechanism of Business Cycles

This paper suggests that business cycles may be a manifestation of coupled real economy and stock market dynamics and describes a mechanism that can generate economic fluctuations consistent with observed business cycles. To this end, we seek to incorporate into the macroeconomic framework a dynamic stock market model based on opinion interactions (Gusev et al., 2015). We derive this model from microfoundations, provide its empirical verification, demonstrate that it contains the efficient market as a particular regime and establish a link through which macroeconomic models can be attached for the study of real economy and stock market interaction. To examine key effects, we link it with a simple macroeconomic model (Blanchard, 1981). The coupled system generates nontrivial endogenous dynamics, which exhibit deterministic and stochastic features, producing quasiperiodic fluctuations (business cycles). We also inspect this system’s behavior in the phase space. The real economy and the stock market coevolve dynamically along the path governed by a stochastically-forced dynamical system with two stable equilibria, one where the economy expands and the other where it contracts, resulting in business cycles identified as the coherence resonance phenomenon. Thus, the incorporation of stock market dynamics into the macroeconomic framework, as presented here, allows the derivation of realistic behaviors in a tractable setting.

Evolutionary dynamics of the prisoner's dilemma with expellers

Expulsion refers to the widespread behavior of expelling intruders from the owners’ territories, which has not been considered in current models on the evolutionary dynamics of cooperation so far. In the context of prisoner’s dilemma, we present a simple game-theoretical model of expulsion in which punishing cooperators (i.e. expellers) are able to banish defectors from their own neighborhoods. In the mean-field limit, our theoretical analysis of prisoner’s dilemma with expellers shows that the increment of either vacant sites ratio or time scale parameter between pairwise interaction process and strategy updating process can slow down evolutionary speed though defection is the only stable fixed point anyway. In more realistic spatial settings, we provide both analytical and numerical results for the limiting case where pairwise interaction dynamics proceeds much faster than strategy updating dynamics. Using the extended pair approximation methods and Monte Carlo simulations, we show that the introduction of expellers not only promotes coevolution of expulsion and cooperation by means of both direct and indirect domain competition but also opens the gate to rich dynamical behaviors even if expulsion is costly. Phase diagrams reveal the occurrence of frozen as well as dynamical stationary states, between which continuous or discontinuous phase transition may happen. For intermediate ranges, we investigate numerically the coupled interplay between pairwise interaction dynamics and strategy updating dynamics, and show that the validity of main results for the limiting case can be extended to this general case. Interestingly, there exists an optimal value of time scale parameter that results in the maximum fraction of altruistic players, which resembles the coherence resonance phenomenon in dynamical systems. Our results may provide insights into understanding coevolutionary dynamics of expulsive and cooperative behavior in social dilemma situations.