Small-world Neuronal Networks Research Articles

Dynamical behaviors in discrete memristor-coupled small-world neuronal networks

The brain is a complex network system in which a large number of neurons are widely connected to each other and transmit signals to each other. The memory characteristic of memristors makes them suitable for simulating neuronal synapses with plasticity. In this paper, a memristor is used to simulate a synapse, a discrete small-world neuronal network is constructed based on Rulkov neurons and its dynamical behavior is explored. We explore the influence of system parameters on the dynamical behaviors of the discrete small-world network, and the system shows a variety of firing patterns such as spiking firing and triangular burst firing when the neuronal parameter α is changed. The results of a numerical simulation based on Matlab show that the network topology can affect the synchronous firing behavior of the neuronal network, and the higher the reconnection probability and number of the nearest neurons, the more significant the synchronization state of the neurons. In addition, by increasing the coupling strength of memristor synapses, synchronization performance is promoted. The results of this paper can boost research into complex neuronal networks coupled with memristor synapses and further promote the development of neuroscience.

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.

Coherence resonance modulated by hybrid synapses and time delay in modular small-world neuronal networks with E–I balanced state

Coherence resonance modulated by hybrid synapses and time delay in modular small-world neuronal networks with E–I balanced state

The power law statistics of the spiking timing in a neuronal network

Information encoding and decoding by neurons is a fundamental process in neuroscience. Herein, we present a statistical investigation of the first spike timing arising from the neuronal population in a small-world network with the Hodgkin–Huxley model after a neuron has received current stimulation, including a transient or a continuous stimulus. Regardless of how the interaction between neurons in the network was implemented, via electrical coupling or chemical synapses, we found the same power-law statistics for the first spike timing, independent of the topological structure of the neuronal network. We further suggest that such power-law statistics can be a generalized feature for the first spike timing in the small-world and scale-free neuronal networks. Our findings provide new insight into the coding mechanism for the first spike timing and improve the understanding of the power-law behavior in nature.

Effects of feedback control in small-world neuronal networks interconnected according to a human connectivity map

In this work, we consider a phenomenological two-dimensional discrete model coupled in a structure of a clustered network to investigate the suppression of neuronal synchronization in a complex network. We constructed a network according to a weighted human connectivity matrix and an adjacency matrix that carries small-world properties. The coupling between neurons is inserted through a chemical synapse term and a neuronal activation function. The neuronal synchronization is measured by the Kuramoto order parameter. We intend to achieve the suppression of burst phase synchronization, and for that, we use a mathematical tool, based on the technique of deep brain stimulation, which consists of applying an external signal to the network after a certain time, causing the bursts to desynchronize. Our results are efficient when applying the feedback method both in the global network and in the cortical regions. We have seen that for cortical regions, synchronization is more difficult to suppress, however, by slightly increasing the perturbation, we are able to achieve the desired effect. This shows that it is possible to use the control efficiently in isolated cortical areas, therefore, we present a new alternative to conventional methods, avoiding to apply the control to the entire network to obtain the same results.

Temperature-controlled propagation of spikes in neuronal networks

Temperature plays a vital role in the functioning of biological organisms and there often exists an optimal temperature for their best performance. In this work, we investigate the role of temperature on spike propagation in scale-free and small-world neuronal networks, where a single neuron is chosen randomly for receiving a stimulus current. Upon exploiting the dominant phase-advanced driving (DPAD) method, the complex neuronal network is seen as a regular feed-forward multilayer neuronal network. The propagation route is then clearly identified, and many traveling-like waves are formed along the propagation route. Interestingly, we find that temperature not only controls the shortest path of propagation but also regulates the response time of a single neuron. The propagation speed is also maximized for an optimal choice of temperature at which the spike rapidly propagates through the entire neuronal network. Our findings extend the current understanding of the neuronal networks functioning and provide new insights into the existence of an optimal temperature as seen in our experiments on several living biological systems.

Transmission of pacemaker signal in a small world neuronal networks: temperature effects

Transmission of pacemaker signal in a small world neuronal networks: temperature effects

Chimera states in coupled Hindmarsh-Rose neurons with α-stable noise

In this paper, we study α-stable noise-induced chimera states in a small-world Hindmarsh-Rose neuronal network. Chimera states are the coexistence of coherence and incoherence. The α-stable noise is a general non-Gaussian noise, and can be used to describe more complex and changeable noisy environments. We focus on the effect of the parameters of the small-world network (the rewiring probability) and α-stable noise (the stability parameter and noise intensity) on the chimera state. We find that the changes of the rewiring probability, the stability parameter and noise intensity can make the location and range of the incoherence domain for the chimera state shift and change, and changes of the stability parameter and noise intensity even make chimera state disappear. Moreover, we propose the strength of coherence based on the local order parameter, and it can be used to identify not only the occurrence of chimera states but also the proportion of coherent neurons in the entire network.

Impacts of autapse on chaotic resonance in single neurons and small-world neuronal networks.

Chaotic resonance (CR) is a new phenomenon induced by an intermediate level of chaotic signal intensity in neuronal systems. In the current study, we investigated the effects of autapse on the CR phenomenon in single neurons and small-world (SW) neuronal networks. In single neurons, we assume that the neuron has only one autapse modelled as electrical, excitatory chemical and inhibitory chemical synapse, respectively. Then, we analysed the effects of each one on the CR, separately. Obtained results revealed that, regardless of its type, autapse significantly increases the chaotic resonance of the appropriate autaptic parameter's values. It is also observed that, at the optimal chaotic current intensity, the multiple CR emerges depending on autaptic time delay for all the autapse types when the autaptic delay time or its integer multiples match the half period or period of the weak signal. In SW networks, we investigated the effects of chaotic activity on the prorogation of pacemaker activity, where pacemaker neurons have different kinds of autapse as considered in single neuron cases. Obtained results revealed that excitatory and electrical autapses prominently increase the prorogation of pacemaker activity, whereas inhibitory autapse reduces or does not change it. Also, the best propagation was obtained when the autapse was excitatory. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.

Pattern transition of neuronal networks induced by chemical autapses with random distribution

Abstract The difference of congenital inheritance and acquired development makes the autaptic distribution in different brain regions variant. To investigate the physiological regulation of autaptic structures on the nervous system, the effects of chemical autapses with random distribution on the dynamics of Newman-Watts small-world neuronal networks are systematically analyzed with the help of three network metrics. The autaptic occurring probability is first introduced to characterize the random distribution of autaptic structures. Numerical results show that the random distribution of chemical autapses can markedly modulate the electrophysiological activities of neuronal networks owing to the self-feedback function of excitatory autapses, not only promoting the transmission of neural signals, but also inducing the network-level stochastic resonance and the transition of network dynamics. Particularly, the autaptic random distribution can make subthreshold or chaotic neuronal networks generate the phase synchronization phenomena and eventually evolve into the synchronous periodic discharge state, which provides a strategy to achieve the complete synchronization through pattern transition. This study reveals the ability of the stochastic characteristics of autaptic structures to alter the evolution of network spatiotemporal patterns, which could contribute to the application of autaptic structures in physiological experiments or artificial neural networks.

Pattern control of external electromagnetic stimulation to neuronal networks

The application of external electromagnetic stimulation to regulate the electrophysiological activities of specific brain regions can provide an ideal control or treatment scheme for some non-organic mental diseases. To further explore the effectiveness of electromagnetic stimulation in the treatment of mental illnesses, the regulatory abilities of external electromagnetic stimulation on the pattern dynamics of Newman–Watts small-world neuronal networks are systematically studied. The main stability function is used to construct four periodic or chaotic synchronous networks. Also, the average discharge frequency and the consistency coefficient are selected to measure the regulatory effects of external electromagnetic stimulation on the network dynamics. Numerical experiments show that electromagnetic stimulation can inhibit the electrophysiological activities of neuronal networks. Periodic electromagnetic stimulation with large amplitude or stochastic electromagnetic stimulation with large deviation has a more significant inhibitory effect on the discharge activities, not only effectively desynchronizing the discharge activities, but also controlling the evolution of spatiotemporal patterns, and even inducing the synchronization transition. Additionally, the number of stimulated neurons in neuronal networks also plays an important role in the evolution of spatiotemporal patterns. This study could provide theoretical guidance for the physiological application of electromagnetic stimulation in the treatment of certain mental diseases.

Controlling a complex system near its critical point via temporal correlations

Many complex systems exhibit large fluctuations both across space and over time. These fluctuations have often been linked to the presence of some kind of critical phenomena, where it is well known that the emerging correlation functions in space and time are closely related to each other. Here we test whether the time correlation properties allow systems exhibiting a phase transition to self-tune to their critical point. We describe results in three models: the 2D Ising ferromagnetic model, the 3D Vicsek flocking model and a small-world neuronal network model. We demonstrate that feedback from the autocorrelation function of the order parameter fluctuations shifts the system towards its critical point. Our results rely on universal properties of critical systems and are expected to be relevant to a variety of other settings.

Synchronization and Rhythm Transition in a Complex Neuronal Network

Synchronization and rhythm transition in an excitatory-inhibitory balanced cortical neuronal network are investigated in this paper. A small-world neuronal network is performed to be the cortical region of cerebral cortex, which is composed of different types of Izhikevich neurons. The combination of regular spiking (RS) cells, chattering (CH) cells, or mixed RS and CH cells are imitated as excitatory neurons, whereas fast spiking (FS) cells mimic inhibitory neurons. We mainly focus on the effect of different types of neurons on synchronization and rhythm transition of the neuronal network. The simulation results illustrate that it is easier for the neuronal network with CH excitatory neurons to achieve synchronization, and it is also more susceptible to the parameters than the network with RS neurons. Together with the weight of the synaptic connection, the structure of the small-world network is also explored to identify its influence on the synchronization and the rhythm transition. Moreover, we found that the synchronization performance could be improved by increasing the degree of influence among neurons. Importantly, the synchronization states are associated with the rhythm transitions. Especially, the consistency of synchronization of the neuronal network and y band rhythm is illustrated. In addition, our results could have an important significance on further understanding brain rhythms and synchrony in neuroscience.

Synchronous Dynamics in Multilayer Memristive Neural Networks: Effect of Electromagnetic Induction

Brain has a hierarchical structure with multiple connection types. To further explore the effect of electromagnetic induction on biological neural networks, in this paper, a two-layer small-world neuronal network with electrical intra-layer connections and memristive inter-layer connections was constructed. In specially, the two layer have different spiking and bursting activities. Electrical coupling strength and electromagnetic induction coefficient are taken as control parameter. Numerical results indicate that the two-layer neurons in different discharge states can achieve synchronization and the firing patterns of the synchronized neurons are related to the electromagnetic induction. Moreover, some particular dynamical states including chimera state and bursting transition are observed in the network. Then, the mechanisms of the two burst transitions are clarified. In addition, the statistical synchronization factor and average error are introduced to measure the intra-layer and inter-layer synchronization, respectively, which reveal that electrical coupling induces and enhances the synchronization more effectively for a higher electromagnetic induction coefficient. Our obtained results indicate that the electromagnetic induction exerts significant impact in modulating the dynamic behavior of neural networks, and provide a useful guidance on the study of physiological functions related to synchronization in the brain.

Emergence of spatially periodic diffusive waves in small-world neuronal networks.

It has been observed in experiment that the anatomical structure of neuronal networks in the brain possesses the feature of small-world networks. Yet how the small-world structure affects network dynamics remains to be fully clarified. Here we study the dynamics of a class of small-world networks consisting of pulse-coupled integrate-and-fire (I&F) neurons. Under stochastic Poisson drive, we find that the activity of the entire network resembles diffusive waves. To understand its underlying mechanism, we analyze the simplified regular-lattice network consisting of firing-rate-based neurons as an approximation to the original I&F small-world network. We demonstrate both analytically and numerically that, with strongly coupled connections, in the absence of noise, the activity of the firing-rate-based regular-lattice network spatially forms a static grating pattern that corresponds to the spatial distribution of the firing rate observed in the I&F small-world neuronal network. We further show that the spatial grating pattern with different phases comprise the continuous attractor of both the I&F small-world and firing-rate-based regular-lattice network dynamics. In the presence of input noise, the activity of both networks is perturbed along the continuous attractor, which gives rise to the diffusive waves. Our numerical simulations and theoretical analysis may potentially provide insights into the understanding of the generation of wave patterns observed in cortical networks.

Effects of electromagnetic induction on vibrational resonance in single neurons and neuronal networks

In this paper, Vibrational Resonance (VR), in which the response of some dynamical systems to a weak, low frequency signal can be enhanced by the optimal amplitude of high frequency signal, is investigated under the effects of electromagnetic induction in both single neurons and small-world networks. We find that the occurrence of VR in single neurons requires less energy in the presence of electromagnetic induction, although the resonant peak of the response reduces. Besides, VR can be obtained in small-world networks both with and without electromagnetic induction. In small-world neuronal networks, the highest resonance peak of VR enhances with an increase in the probability of adding link in case of without electromagnetic induction. On the other hand, with the increasing of the probability of adding link, VR disappears in the presence of relatively strong electromagnetic induction, while it enhances in the presence of relatively weak electromagnetic induction.

Inhibitory-autapse-enhanced signal transmission in neural networks

The multi-frequency hybrid signal is an important stimulus from the external environment on the neuronal networks for detection. The mechanism of the detection may be understood by the vibrational resonance, in which the moderate intensity of high-frequency force can amplify the response of neuronal systems to the low-frequency signal. In this paper, the effects of electrical and chemical autapses on signal transmission are investigated in scale-free and small-world neuronal networks, where an external two-frequency signal is introduced only to one neuron as a pacemaker. We observed that the inhibitory autapse can significantly enhance the signal propagation by the vibrational resonance, while the electrical and excitatory autapses typically weaken the signal transmission, indicating that the inhibitory autapse is more beneficial to transmit the rhythm of the pacemaker to the whole networks. These findings contribute to our understanding of signal detection and information processing in the autapic neuronal system.

Effects of coupling strength and network topology on signal detection in small-world neuronal networks

We study the effects of different coupling strengths and network topologies on signal detection in small-world neuronal networks. Research has previously revealed that the ability of detecting subthreshold signals could be significantly enhanced by appropriately fine-tuning the noise intensity. Here we show that the coupling strength and the structure of the underlying network can also lead toward enhanced signal detection. In particular, we show that there are two levels of the coupling strength at which the subthreshold signal can be detected at an appropriate noise intensity and network structure. We also show that the network structure has little impact on signal detection if the coupling is weak. On the other hand, for intermediate coupling strengths, we show that the shorter the average path length, the better the signal detection. Finally, if the coupling is strong, we show that there exists an intermediate average path length at which signal detection becomes optimal.

Delay-induced synchronization transition in a small-world neuronal network of FitzHugh–Nagumo neurons subjected to sine-Wiener bounded noise

Noise and delay are ubiquitous in brain and they have significant effects on neuronal network synchronization and even brain functions. Based on a small-world neuronal network of delayed FitzHugh–Nagumo (FHN) neurons subjected to sine-Wiener (SW) bounded noise, the effects of delay and SW noise on synchronization and synchronization transition are numerically investigated by calculating a synchronization measure R and plotting spatiotemporal patterns. The phenomenon of delay-induced synchronization transition is observed as delay [Formula: see text] is increased. And large self-correlation time and strength of SW noise can increase the number of delay-induced synchronization transition. In addition, delay-induced synchronization transition is robust against the change of topology structure of neuronal network and this phenomenon becomes much easier to see for small nearest neighbors k in the small-world network. Since synchronization transition may imply functional switch, our results may have important implications, and inspire future studies.

Enhancement of temporal regularity and degradation of spatial synchronization induced by cross-correlated sine-Wiener noises in regular and small-world neuronal networks

Most previous studies assumed noise to be unbounded Gaussian. Here the effects of non-Gaussian cross-correlated sine-Wiener (CCSW) bounded noises on temporal regularity and spatial synchronization of coupled neurons are investigated in regular and small-world networks of the FitzHugh–Nagumo (FHN) neurons. For regular neuronal networks, as cross-correlation time of CCSW noises is increased, CCSW noises-induced temporal coherent resonance occurs at appropriately cross-correlation time of CCSW noises, and spatial synchronization in neuronal network is always impaired. In addition, the increasing degree of correlation of CCSW noises may enhance or impair temporal regularity, which is dependent on cross-correlation time. On the other hand, the increasing degree of correlation of CCSW noises destroys spatial synchronization or has no effect on spatial synchronization. For small world neuronal network, CCSW noises-induced enhancement of temporal regularity and degradation of spatial synchronization are still observed. Furthermore, the increasing rewiring probability make spatiotemporal pattern more order in time and in space. If delay is introduced into small world network, the aforementioned CCSW noises-induced phenomena still exist. Meanwhile, delay let spatiotemporal pattern more disorder.