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![Example of small-world network topologies with 20 neurons. The rewiring parameter p is set as p=0.1,0.5,1.0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p= 0.1, 0.5, 1.0$$\end{document} from left to right](publication/299356396/figure/fig1/AS:941798503510021@1601553669635/Example-of-small-world-network-topologies-with-20-neurons-The-rewiring-parameter-p-is.gif)
Example of small-world network topologies with 20 neurons. The rewiring parameter p is set as p=0.1,0.5,1.0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p= 0.1, 0.5, 1.0$$\end{document} from left to right
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Neural electrical activities are due to the movement of ions in/out of the neuron and can be modulated by an external electric field. Moreover, clinical evidences reveal that the modulated activities of brain tissue by an external electric field are associated with normal or pathological brain functions. In this paper, we investigated the spatiotem...
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... Many studies have shown that time delays can both facilitate and disrupt the synchronization of neural networks (Dhamala et al., 2004;Guo et al., 2012;Wu et al., 2023). In addition, other factors, such as synaptic type and coupling strength, are considered important (Wang HT and Chen, 2016;Lu et al., 2017;Xu YM et al., 2019). ...
Time delay and coupling strength are important factors that affect the synchronization of neural networks. In this study, a modular neural network containing subnetworks of different scales was constructed using the Hodgkin–Huxley (HH) neural model; i.e., a small-scale random network was unidirectionally connected to a large-scale small-world network through chemical synapses. Time delays were found to induce multiple synchronization transitions in the network. An increase in coupling strength also promoted synchronization of the network when the time delay was an integer multiple of the firing period of a single neuron. Considering that time delays at different locations in a modular network may have different effects, we explored the influence of time delays within each subnetwork and between two subnetworks on the synchronization of modular networks. We found that when the subnetworks were well synchronized internally, an increase in the time delay within both subnetworks induced multiple synchronization transitions of their own. In addition, the synchronization state of the small-scale network affected the synchronization of the large-scale network. It was surprising to find that an increase in the time delay between the two subnetworks caused the synchronization factor of the modular network to vary periodically, but it had essentially no effect on the synchronization within the receiving subnetwork. By analyzing the phase difference between the two subnetworks, we found that the mechanism of the periodic variation of the synchronization factor of the modular network was the periodic variation of the phase difference. Finally, the generality of the results was demonstrated by investigating modular networks at different scales.
... Hence, studying the firing behavior of neurons under external stimulus plays a positive role in understanding the pathogenesis of neuronal diseases and then contributes to the treatment and prevention of such neurological diseases. It has been proved that the dynamics of a neuron or neural network can be affected by external stimulus, such as noise [11], electric field [12], and magnetic field. At the same time, EMR has become a factor that cannot be ignored because it is almost full of human living environment. ...
External stimulus has an impact on the functional behavior of the biological nervous system, and appropriate stimulus helps the organism to maintain neural function. Inspired by this, the effects of different external stimuli on the dynamical behaviors of neuron model are studied in this paper. Firstly, a fractional-order (FO) memristor-coupled tabu learning two-neuron model whose equilibrium points are symmetric about the origin and unstable is constructed. The dynamical behaviors of this neuron model under different stimuli are further discussed, which are no external stimulus, external forced current stimulus, and electromagnetic radiation (EMR), respectively. The neuron model without external stimulus has periodic attractors and transient chaos, but applying external stimulus to one of the neurons can produce abundant two-scroll chaotic attractors and multistability; especially, when the neuron model is stimulated by EMR, it can generate hyperchaotic attractors that have not been observed in the tabu learning neuron model before. Besides, the transient transition behaviors of the model under different stimuli are also studied. Then, a pseudo-random number generator is designed and its random performance is tested with NIST suite. Finally, it is applied to voice encryption, and the result shows that it has good encryption effect. Therefore, it can be said that the FO memristor-coupled tabu learning two-neuron model has superior randomness and is suitable for chaotic-based engineering applications.
... Guo et al. [71] investigated the intrinsic coding mechanism of signals in neurons by adding Gaussian white noise to auditory neurons. Wang et al. [72] examined the effect of external electric fields on the synchronization of neuronal network systems in the presence of Gaussian white noise. ...
The ambient temperature and the time delay of signal transmission are very important influences on the synchronization behavior of neuronal networks. In this paper, a neuronal network with the power-law degree distribution is constructed using a Hodgkin–Huxley model containing a temperature modulation factor and noise, and neurons at each node of the scale-free network are interconnected by electrical and chemical synapses, respectively. In scale-free networks with different ambient temperatures, the absence of time delay causes the synchronization of networks connected by both synaptic types to increase with coupling strength at lower temperatures, while the opposite is shown for networks connected by chemical synapses at higher temperatures. Networks connected by both synaptic types show multiple synchronization transitions when there is the time delay. Surprisingly, there is a temperature threshold for scale-free networks connected by chemical synapses, beyond which synchronization becomes very poor. By introducing the coefficient of variation and the mean inter-spikes intervals, it is found that the emergence of temperature thresholds for networks connected by chemical synapses is caused by a further increase in the difference in firing frequency of neurons due to increasing temperature. Finally, the generality of the results and mechanisms studied in scale-free networks is verified by investigating the effects of different network scales on synchronization.
... In general, the coupled neurons are connected by different kinds of types, such as the chain, small-world, regular network. Then, the collective dynamics between coupled neurons under different conditions are discussed, for example, the feedback control [14], forcing currents, noise [15][16][17][18], time delay [19], electromagnetic radiation, electric fields [20], as well as optical and audio signals. It has been proven that the external stimuli could change the membrane potential of neurons, inducing different firing patterns and dynamical behaviors. ...
... For example, Ref. [19] stated that the dynamical behaviors of asynchrony resonance could be observed under different time delay forms. Wang et al. [20] investigated the effect of the AC electric field on the dynamical activities of the neuron network. Zhang et al. [23] discussed the synchronization between memristive oscillators without direct variable coupling, and declared the mechanism that the resonance could be induced between oscillators due to the energy injection. ...
Photosensitive neurons can capture and convert external optical signals, and then realize the encoding signal. It is confirmed that a variety of firing modes could be induced under optical stimuli. As a result, it is interesting to explore the mode transitions of collective dynamics in the photosensitive neuron network under external stimuli. In this work, the collective dynamics of photosensitive neurons in a small-world network with non-synaptic coupling will be discussed with spatial diversity of noise and uniform noise applied on, respectively. The results prove that a variety of different collective electrical activities could be induced under different conditions. Under spatial diversity of noise applied on, a chimera state could be observed in the evolution, and steady cluster synchronization could be detected in the end; even the nodes in each cluster depend on the degree of each node. Under uniform noise applied on, the complete synchronization window could be observed alternately in the transient process, and steady complete synchronization could be detected finally. The potential mechanism is that continuous energy is pumped in the phototubes, and energy exchange and balance between neurons to form the resonance synchronization in the network with different noise applied on. Furthermore, it is confirmed that the evolution of collective dynamical behaviors in the network depends on the external stimuli on each node. Moreover, the bifurcation analysis for the single neuron model is calculated, and the results confirm that the electrical activities of single neuron are sensitive to different kinds of noise.
... Indeed, the electrophysiological environments in the brain are very complex. 46,47 Therefore, it is essential to explore the dynamics of the HNN that is simulated by electromagnetic induction and electromagnetic radiation concurrently, which has not been reported until now. ...
Due to the potential difference between two neurons and that between the inner and outer membranes of an individual neuron, the neural network is always exposed to complex electromagnetic environments. In this paper, we utilize a hyperbolic-type memristor and a quadratic nonlinear memristor to emulate the effects of electromagnetic induction and electromagnetic radiation on a simple Hopfield neural network (HNN), respectively. The investigations show that the system possesses an origin equilibrium point, which is always unstable. Numerical results uncover that the HNN can present complex dynamic behaviors, evolving from regular motions to chaotic motions and finally to regular motions, as the memristors' coupling strength changes. In particular, coexisting bifurcations will appear with respect to synaptic weights, which means bi-stable patterns. In addition, some physical results obtained from breadboard experiments confirm Matlab analyses and Multisim simulations.
... Indeed, general anesthesia with neuromuscular blockade must be administered for these procedures, due to the severe muscle contractions that occur with the administration of IRE pulses. The induced TMP reaches the threshold of action potentials in nearby nerves [103][104][105][106]. ...
Electroporation-based therapy (EBT), as a high-voltage-pulse technology has been prevalent with favorable clinical outcomes in the treatment of various solid tumors. The aim of this review paper is to promote the clinical translation of EBT for brain tumors. First, we briefly introduced the mechanism of pore formation in a cell membrane activated by external electric fields using a single cell model. Then, we summarized and discussed the current in vitro and in vivo preclinical studies, in terms of (1) the safety and effectiveness of EBT for brain tumors in animal models, and (2) the blood-brain barrier (BBB) disruption induced by EBT. Two therapeutic effects could be achieved in EBT for brain tumors simultaneously, i.e., the tumor ablation induced by irreversible electroporation (IRE) and transient blood-brain barrier (BBB) disruption induced by reversible electroporation (RE). The BBB disruption could potentially improve the uptake of anti-tumor drugs thereby enhancing brain tumor treatment. The challenges that hinder the application of EBT in the treatment of human brain tumors are discussed in the review paper as well.
... An appropriate external stimulus can change the firing patterns of neurons. Much research in recent years has focused on the effects of electromagnetic radiation on neuronal behaviors [16][17][18][19][20]. Electromagnetic radiation can affect the dynamic characteristics of neurons, and electrical or electromagnetic stimulation can also be used to treat neurological diseases [21][22][23]. ...
The dynamics of neuronal firing activity is vital for understanding the pathological respiratory rhythm. Studies on electrophysiology show that the magnetic flow is an essential factor that modulates the firing activities of neurons. By adding the magnetic flow to Butera’s neuron model, we investigate how the electric current and magnetic flow influence neuronal activities under certain parametric restrictions. Using fast-slow decomposition and bifurcation analysis, we show that the variation of external electric current and magnetic flow leads to the change of the bistable structure of the system and hence results in the switch of neuronal firing pattern from one type to another.
... Most of the researches on the energy evolution of neurons focus on the neuron model itself, without considering the influence of electromagnetic field on the neuron system [62,63]. The electrical activities of neuron depend on the complex electrophysiological conditions in the neuron system, which shows that the complex distribution of electromagnetic field can be detected in the neuron system [64][65][66]. Due to the internal bioelectricity effect of the nervous system, the dynamic behavior of each neuron in the electrical activity can be changed according to Maxwell electromagnetic induction theorem [67,68]. ...
The FitzHugh-Nagumo (FHN) neural model is widely used to study the dynamic characteristics of signal propagation, synchronization, stochastic resonance(SR), coherent resonance(CR), and bifurcation of neurons. Based on Helmholtz theorem and the FHN neuron model, the expression of Hamilton energy function of FHN neural model driven by high-low frequency(HLF) electromagnetic radiation is derived. The correctness and uniqueness of the analytical solution are verified by using the constraints, and the electrical activities and Hamilton energy function of neuron are discussed by numerical simulations. It is found that electrical activity mode of FHN neuron undergoes a succession transition of quiescent state, spiking state, bursting state, and mixed state by changing the parameters such as the intensity of the external forcing current, the amplitude and angular frequency of HLF signal. The electrical activities process of FHN neuron is accompanied by the storage and release of system energy, this result may provide an understanding of the coding and conversion of electrical activity from the perspective of the relevance and dependence of energy costs.
... It has been confirmed that several factors including network structure [5,6] , time delay [7] , noise [8] and electric field [9] can change the dynamics of a neural network. Particularly, electromagnetic radiation is one of the factor that cannot be ignored, which is almost full of the human living environment due to the widely application of various electromagnetic communication instruments. ...
Electromagnetic radiation has an effect on the functional behavior of nervous system, and appropriate electromagnetic radiation is helpful to treat some neurological diseases. In this article, we investigate the effects of electromagnetic radiation distribution on the nonlinear dynamics of a neural network with n neurons. A new mathematical model of the neural network under electromagnetic radiation is developed and analyzed, where electromagnetic radiation is equivalent to the magnetic flux passing through the cell membrane. Chaotic dynamics of the nerve system is detailedly studied by stimulating different number of neurons in the neural network model consisted of three neurons. It is proved that with the increasing of the number of neurons stimulated by electromagnetic radiation, the dynamics behaviors of the neural network gradually change from period moving to chaos, transient chaos and intricate hyperchaos. That is, the dynamical behaviors of the neural system can be modulated through changing the number of neurons affected by electromagnetic radiation in neural network. Therefore, it could give new insights to understand the occurrence mechanism of some neuronal diseases. Moreover, a flexible hardware circuit of the neural network with different electromagnetic radiation distribution is implemented by using commercially available electronic elements, and the experimental measurements are consistent with numerical simulation results.
... Influence of external electric or magnetic fields or both on the neuronal environment can also be treated as noise. Wang and Chen [14] identified that strong external electric field can influence the firing rate and synchronization of neural networks. Many theoretical and experimental studies have proved that both static and dynamic magnetic fields can suppress neuronal activities and cell growth [15][16][17][18][19]. ...
... which measures the mean of average spikes (F i ) generated by the N neurons of the network during the simulation [14]. Here, F i is the number of spikes generated by the ith neuron in 1 ms. ...
Near-death spikes or near-death surges are a sudden increase in neuron activity in the human brain before neurons end their firings. Just before a person is clinically dead, such spikes are observed in certain cases, so the name is near-death spikes. The reason for this behavior is the lack of oxygen in brain (Chawla et al. in J Palliat Med 12(12):1095–1100, 2009). In this study, it is demonstrated that a particular type of noise called Lévy noise can generate such activity in the neural network of the worm Caenorhabditis elegans. The study identified different parameter regions of noise at which the network makes transitions from one synchronous state to another and the mechanism behind them. Such transitions are already reported in cortical regions of brain (Canavero et al. in Surg Neurol Int 7(Suppl 24):S623–S625, 2016). During the transition period between asynchronous and synchronous firing states, network is more susceptible to changes in firing pattern of individual neurons (Zandt et al. in PLoS ONE 6(7):e22127, 2011; Uzuntarla et al. Neural Netw 110:131–140, 2019). In this work, it is demonstrated that the recognized parameter regions can be used to control the network dynamics. The study also identified Lévy noise values at which the network displays generation of waves of different frequencies. This result suggests a new method for neurostimulation in the case of traumatic brain injury. The study reveals that the characteristic exponent (\(\alpha \)) of the noise has better influence on the network dynamics than the scale parameter of noise (D) and the synaptic coupling constant (Gsyn) of the network. The neuronal network even displayed Gamma oscillations for large values of \(\alpha \). If the parameters of the neurons are made chaotic, the network firing rate is diminished and it displayed Delta and Theta oscillations.
