Lévy noise improves the electrical activity in a neuron under electromagnetic radiation

[The inverse stochastic resonance in a small-world neuronal network under electromagnetic stimulation]

Electromagnetic stimulation is an important neuromodulation technique that modulates the electrical activity of neurons and affects cortical excitability for the purpose of modulating the nervous system. The phenomenon of inverse stochastic resonance is a response mechanism of the biological nervous system to external signals and plays an important role in the signal processing of the nervous system. In this paper, a small-world neural network with electrical synaptic connections was constructed, and the inverse stochastic resonance of the small-world neural network under electromagnetic stimulation was investigated by analyzing the dynamics of the neural network. The results showed that: the Levy channel noise under electromagnetic stimulation could cause the occurrence of inverse stochastic resonance in small-world neural networks; the characteristic index and location parameter of the noise had significant effects on the intensity and duration of the inverse stochastic resonance in neural networks; the larger the probability of randomly adding edges and the number of nearest neighbor nodes in small-world networks, the more favorable the anti-stochastic resonance was; by adjusting the electromagnetic stimulation parameters, a dual regulation of the inverse stochastic resonance of the neural network can be achieved. The results of this study provide some theoretical support for exploring the regulation mechanism of electromagnetic nerve stimulation technology and the signal processing mechanism of nervous system.

Influence of inhibitory autapses on synchronization of inhibitory network gamma oscillations

A recent experimental study showed that inhibitory autapses favor firing synchronization of parvalbumin interneurons in the neocortex during gamma oscillations. In the present paper, to provide a comprehensive and deep understanding to the experimental observation, the influence of inhibitory autapses on synchronization of interneuronal network gamma oscillations is theoretically investigated. Weak, middle, and strong synchronizations of a globally inhibitory coupled network composed of Wang-Buzsáki model without autapses appear at the bottom-left, middle, and top-right of the parameter plane with the conductance (gsyn) and the decay constant (τsyn) of inhibitory synapses taken as the x-axis and y-axis, respectively. After introducing inhibitory autapses, the border between the strong and middle synchronizations in the (gsyn, τsyn) plane moves to the top-right with increasing the conductance (gaut) and the decay constant (τaut) of autapses, due to that interspike interval of the single neuron becomes longer, leading to that larger τsyn is needed to ensure the strong synchronization. Then, the synchronization degree of middle and strong synchronizations around the border in the (gsyn, τsyn) plane decreases, while of strong synchronization in the remaining region remains unchanged. The synchronization degree of weak synchronization increases with increasing τaut and gaut, due to that the inhibitory autaptic current becomes strong and long to facilitate synchronization. The enhancement of weak synchronization modulated by inhibitory autapses is also simulated in the random, small-world, and scale-free networks, which may provide explanations to the experimental observation. These results present complex dynamics of synchronization modulated by inhibitory autapses, which needs future experimental demonstrations.

Control of noise-induced coherent oscillations in three-neuron motifs

The phenomenon of self-induced stochastic resonance (SISR) requires a nontrivial scaling limit between the deterministic and the stochastic timescales of an excitable system, leading to the emergence of coherent oscillations which are absent without noise. In this paper, we numerically investigate SISR and its control in single neurons and three-neuron motifs made up of the Morris–Lecar model. In single neurons, we compare the effects of electrical and chemical autapses on the degree of coherence of the oscillations due to SISR. In the motifs, we compare the effects of altering the synaptic time-delayed couplings and the topologies on the degree of SISR. Finally, we provide two enhancement strategies for a particularly poor degree of SISR in motifs with chemical synapses: (1) we show that a poor SISR can be significantly enhanced by attaching an electrical or an excitatory chemical autapse on one of the neurons, and (2) we show that by multiplexing the motif with a poor SISR to another motif (with a high SISR in isolation), the degree of SISR in the former motif can be significantly enhanced. We show that the efficiency of these enhancement strategies depends on the topology of the motifs and the nature of synaptic time-delayed couplings mediating the multiplexing connections.

Spontaneous electromagnetic induction promotes the formation of economical neuronal network structure via self-organization process

Developed through evolution, brain neural system self-organizes into an economical and dynamic network structure with the modulation of repetitive neuronal firing activities through synaptic plasticity. These highly variable electric activities inevitably produce a spontaneous magnetic field, which also significantly modulates the dynamic neuronal behaviors in the brain. However, how this spontaneous electromagnetic induction affects the self-organization process and what is its role in the formation of an economical neuronal network still have not been reported. Here, we investigate the effects of spontaneous electromagnetic induction on the self-organization process and the topological properties of the self-organized neuronal network. We first find that spontaneous electromagnetic induction slows down the self-organization process of the neuronal network by decreasing the neuronal excitability. In addition, spontaneous electromagnetic induction can result in a more homogeneous directed-weighted network structure with lower causal relationship and less modularity which supports weaker neuronal synchronization. Furthermore, we show that spontaneous electromagnetic induction can reconfigure synaptic connections to optimize the economical connectivity pattern of self-organized neuronal networks, endowing it with enhanced local and global efficiency from the perspective of graph theory. Our results reveal the critical role of spontaneous electromagnetic induction in the formation of an economical self-organized neuronal network and are also helpful for understanding the evolution of the brain neural system.

Localized nonlinear excitations in diffusive memristor-based neuronal networks

We extend the existing ordinary differential equations modeling neural electrical activity to include the memory effect of electromagnetic induction through magnetic flux, used to describe time varying electromagnetic field. Through the multi-scale expansion in the semi-discrete approximation, we show that the neural network dynamical equations can be governed by the complex Ginzburg-Landau equation. The analytical and numerical envelop soliton of this equation are reported. The results obtained suggest the possibility of collective information processing and sharing in the nervous system, operating in both the spatial and temporal domains in the form of localized modulated waves. The effects of memristive synaptic electromagnetic induction coupling and perturbation on the modulated action potential dynamics examined. Large electromagnetic induction coupling strength may contribute to signal block as the amplitude of modulated waves are observed to decrease. This could help in the development of a chemical brain anaesthesia for some brain pathologies.

Defects formation and spiral waves in a network of neurons in presence of electromagnetic induction

Complex anatomical and physiological structure of an excitable tissue (e.g., cardiac tissue) in the body can represent different electrical activities through normal or abnormal behavior. Abnormalities of the excitable tissue coming from different biological reasons can lead to formation of some defects. Such defects can cause some successive waves that may end up to some additional reorganizing beating behaviors like spiral waves or target waves. In this study, formation of defects and the resulting emitted waves in an excitable tissue are investigated. We have considered a square array network of neurons with nearest-neighbor connections to describe the excitable tissue. Fundamentally, electrophysiological properties of ion currents in the body are responsible for exhibition of electrical spatiotemporal patterns. More precisely, fluctuation of accumulated ions inside and outside of cell causes variable electrical and magnetic field. Considering undeniable mutual effects of electrical field and magnetic field, we have proposed the new Hindmarsh-Rose (HR) neuronal model for the local dynamics of each individual neuron in the network. In this new neuronal model, the influence of magnetic flow on membrane potential is defined. This improved model holds more bifurcation parameters. Moreover, the dynamical behavior of the tissue is investigated in different states of quiescent, spiking, bursting and even chaotic state. The resulting spatiotemporal patterns are represented and the time series of some sampled neurons are displayed, as well.

Complete synchronization of the global coupled dynamical network induced by Poisson noises

The different Poisson noise-induced complete synchronization of the global coupled dynamical network is investigated. Based on the stability theory of stochastic differential equations driven by Poisson process, we can prove that Poisson noises can induce synchronization and sufficient conditions are established to achieve complete synchronization with probability 1. Furthermore, numerical examples are provided to show the agreement between theoretical and numerical analysis.

Response of Electrical Activity in an Improved Neuron Model under Electromagnetic Radiation and Noise

Electrical activities are ubiquitous neuronal bioelectric phenomena, which have many different modes to encode the expression of biological information, and constitute the whole process of signal propagation between neurons. Therefore, we focus on the electrical activities of neurons, which is also causing widespread concern among neuroscientists. In this paper, we mainly investigate the electrical activities of the Morris-Lecar (M-L) model with electromagnetic radiation or Gaussian white noise, which can restore the authenticity of neurons in realistic neural network. First, we explore dynamical response of the whole system with electromagnetic induction (EMI) and Gaussian white noise. We find that there are slight differences in the discharge behaviors via comparing the response of original system with that of improved system, and electromagnetic induction can transform bursting or spiking state to quiescent state and vice versa. Furthermore, we research bursting transition mode and the corresponding periodic solution mechanism for the isolated neuron model with electromagnetic induction by using one-parameter and bi-parameters bifurcation analysis. Finally, we analyze the effects of Gaussian white noise on the original system and coupled system, which is conducive to understand the actual discharge properties of realistic neurons.

Transports in a rough ratchet induced by Lévy noises

We study the transport of a particle subjected to a Lévy noise in a rough ratchet potential which is constructed by superimposing a fast oscillating trigonometric function on a common ratchet background. Due to the superposition of roughness, the transport process exhibits significantly different properties under the excitation of Lévy noises compared to smooth cases. The influence of the roughness on the directional motion is explored by calculating the mean velocities with respect to the Lévy stable index α and the spatial asymmetry parameter q of the ratchet. Variations in the splitting probability have been analyzed to illustrate how roughness affects the transport. In addition, we have examined the influences of roughness on the mean first passage time to know when it accelerates or slows down the first passage process. We find that the roughness can lead to a fast reduction of the absolute value of the mean velocity for small α, however the influence is small for large α. We have illustrated that the ladder-like roughness on the potential wall increases the possibility for particles to cross the gentle side of the ratchet, which results in an increase of the splitting probability to right for the right-skewed ratchet potential. Although the roughness increases the corresponding probability, it does not accelerate the mean first passage process to the right adjacent well. Our results show that the influences of roughness on the mean first passage time are sensitive to the combination of q and α. Hence, the proper q and α can speed up the passage process, otherwise it will slow down it.