Occurrence Of Coherence Resonance Research Articles

Firing behaviors of memristor-based Rulkov neuron map using energy method

Neural firing behavior is essentially the energy transmission between neurons, which can represent the information process of nervous system. Consequently, it is crucial to delve deeply into the intricate firing activity and energy characteristics of neurons. The Helmholtz theorem offers an accurate energy description for continuous neurons. However, the energy of discrete neurons remains under-explored due to lacking an effective theoretical framework. In this paper, we introduce a novel Rulkov neuron map that incorporates a charge-controlled memristor for imitating the effect of electromagnetic radiation. The Hamilton energy method is utilized to investigate the firing behaviors of this neuron map. A pivotal step in our analysis is meticulously scaling the parameters and variables to transform the neuron map into a continuous oscillator, which is essential for obtaining its energy function. In the exploration of the Rulkov neuron map, a range of intricate firing behaviors, including mixed-mode firing, bursting firing and coexistence firing, are observed. Notably, the occurrence of coherence resonance is detected under noise excitation. These behaviors are characterized by the time evolution of membrane potential and Hamilton energy spectrum. Furthermore, FPGA-based experiments are conducted to confirm the numerical results.

Can Lévy noise induce coherence and stochastic resonances in a birhythmic van der Pol system?

The analysis of a birhythmic modified van der Pol type oscillator driven by periodic excitation and Lévy noise shows the possible occurrence of coherence resonance and stochastic resonance. The frequency of the harmonic excitation in the neighborhood of one of the limit cycles influences the coherence of the dynamics on the time scale of the oscillations. The autocorrelation function, the power spectral density and the signal-to-noise-ratio used in this analysis are shown to be maximized for an appropriate choice of the noise intensity. In particular, a proper adjustment of the Lévy noise intensity enhances the output power spectrum of the system, that is, promotes stochastic resonance. Thus, the resonance, as examined using standard measures, seems to occur also in the presence of nonstandard noise. The initial selection of the attractor seems to have an influence on the coherence, while the skewness parameter of the Lévy noise has not a notable impact on the resonant effect.

Effect of inhibitory firing pattern on coherence resonance in random neural networks

The effect of inhibitory firing patterns on coherence resonance (CR) in random neuronal network is systematically studied. Spiking and bursting are two main types of firing pattern considered in this work. Numerical results show that, irrespective of the inhibitory firing patterns, the regularity of network is maximized by an optimal intensity of external noise, indicating the occurrence of coherence resonance. Moreover, the firing pattern of inhibitory neuron indeed has a significant influence on coherence resonance, but the efficacy is determined by network property. In the network with strong coupling strength but weak inhibition, bursting neurons largely increase the amplitude of resonance, while they can decrease the noise intensity that induced coherence resonance within the neural system of strong inhibition. Different temporal windows of inhibition induced by different inhibitory neurons may account for the above observations. The network structure also plays a constructive role in the coherence resonance. There exists an optimal network topology to maximize the regularity of the neural systems.

Coherence resonance of piezoelectric energy harvester with fractional damping

In this paper, we investigate the coherence resonance of a piezoelectric energy harvester of beam subjected to an axial force. The fractional damping is considered. First, a nonlinear model of the energy harvesting system with fractional damping and random excitation is set up. The coupling equations of dynamics and electrics are derived. Euler- Maruyama-Leipnik method is used to solve the fractional order differential equations. The signal-to-noise ratios, mean responses, and other statistical quantities under the damping forces with different orders are computed. The results obviously show the appearance of coherence resonance. It can be seen that the reduction of fractional order not only reduces the critical value of noise level, thus leading to coherence resonance, but also increases the amplitude on the occurrence of coherence resonance. So it is possible to maximize harvest power for a given density or variance of random excitation by varying system parameters.

Effect of Noise Correlation on Noise-Induced Oscillation Frequency in the Photosensitive Belousov–Zhabotinsky Reaction in a Continuous Stirred Tank Reactor

We report on the experimental study of noise-induced oscillations in the photosensitive Ru(bpy)3(2+)-catalyzed Belousov-Zhabotinsky reaction in a continuous stirred tank reactor (CSTR). In the absence of deterministic oscillations and any external periodic forcing, oscillations appear when the system is perturbed by stochastic fluctuations in light irradiation with sufficiently high amplitude in the vicinity of the bifurcation point. The frequency distribution of the noise-induced oscillations is strongly affected by noise correlation. There is a shift of the noise-induced oscillation frequency toward higher frequencies for an intermediate range of the noise correlation exponent, indicating the occurrence of coherence resonance. Our findings indicate that, in principle, noise correlation can be used to direct chemical reactions toward certain behavior.

NON-GAUSSIAN NOISE-INDUCED COHERENCE RESONANCE OF CALCIUM OSCILLATIONS IN BIDIRECTIONALLY COUPLED CELLS

We have studied the effect of a particular kind of non-Gaussian noise (NGN), mainly of its deviation q from Gaussian noise, on the intercellular calcium (Ca2+) oscillations in an array of bidirectionally coupled cells. It is found that as q is increased, the Ca2+ oscillation becomes the most regular at an intermediate optimal q value, representing the occurrence of coherence resonance (CR). This deviation-induced CR behavior shows that the intercellular Ca2+ oscillations of the coupled cells can be enhanced and even optimized by the appropriate NGN. This result provides a new insight into the constructive role of the NGN on the transmission of Ca2+ signaling in coupled cells.

Control of spiking regularity in a noisy complex neural network

The effects of spatiotemporally correlated noise on the regularity of spiking oscillations are studied in a network composed of Fitz-Hugh-Nagumo neurons. The spiking regularity of the neural network becomes the best at a moderate noise intensity, indicating the occurrence of coherence resonance (CR). The CR in a Watts-Strogatz small-world network is further improved by adding a small fraction of long-range connections. Given a set of temporal correlation constant tau and spatial correlation length lambda of the noise, there exists an optimal network topology randomness, at which the spiking oscillations show the best regularity. The optimal randomness of the network topology at different tau and lambda varies in a narrow range. Changing lambda does not affect the optimal tau for achieving the most regular spike train, whereas varying tau, the best spiking regularity emerges at different optimal lambda.

Molecular noise induced circadian oscillation and coherence resonance in the gene network of biological clock

The molecular noise in the gene regulation network of biological clock in Drosophila was studied. Especially, we investigated the effect of molecular noise on the circadian rhythmic oscillation when the system is in the steady state region but only slightly away from the oscillating region. We show that (i) Though the prodution and the decay of the protein are stochastic with the stochastic time interval, the obvious circadian oscillation can be induced depending on the system intrinsic regulation mechanism. (ii) The coherence of molecular noise-induced oscillation is optimal under an appropriate molecular noise level, leading to the occurrence of coherence resonance.

Noise-Induced Coherence and Network Oscillations in a Reduced Bursting Model

The dynamics of the Hindmarsh-Rose (HR) model of bursting thalamic neurons is reduced to a system of two linear differential equations that retains the subthreshold resonance properties of the HR model. Introducing a reset mechanism after a threshold crossing, we turn this system into a resonant integrate-and-fire (RIF) model. Using Monte-Carlo simulations and mathematical analysis, we examine the effects of noise and the subthreshold dynamic properties of the RIF model on the occurrence of coherence resonance (CR). Synchronized burst firing occurs in a network of such model neurons with excitatory pulse-coupling. The coherence level of the network oscillations shows a stochastic resonance-like dependence on the noise level. Stochastic analysis of the equations shows that the slow recovery from the spike-induced inhibition is crucial in determining the frequencies of the CR and the subthreshold resonance in the original HR model. In this particular type of CR, the oscillation frequency strongly depends on the intrinsic time scales but changes little with the noise intensity. We give analytical quantities to describe this CR mechanism and illustrate its influence on the emerging network oscillations. We discuss the profound physiological roles this kind of CR may have in information processing in neurons possessing a subthreshold resonant frequency and in generating synchronized network oscillations with a frequency that is determined by intrinsic properties of the neurons.