Stochastic resonance and synchronization behaviors of excitatory-inhibitory small-world network subjected to electromagnetic induction

The phenomenon of stochastic resonance and synchronization on some complex neuronal networks have been investigated extensively.These studies are of great significance for us to understand the weak signal detection and information transmission in neural systems.Moreover,the complex electrical activities of a cell can induce time-varying electromagnetic fields,of which the internal fluctuation can change collective electrical activities of neuronal networks.However,in the past there have been a few corresponding research papers on the influence of the electromagnetic induction among neurons on the collective dynamics of the complex system.Therefore,modeling each node by imposing electromagnetic radiation on the networks and investigating stochastic resonance in a hybrid network can extend the interest of the work to the understanding of these network dynamics.In this paper,we construct a small-world network consisting of excitatory neurons and inhibitory neurons,in which the effect of electromagnetic induction that is considered by using magnetic flow and the modulation of magnetic flow on membrane potential is described by using memristor coupling.According to our proposed network model,we investigate the effect of induced electric field generated by magnetic stimulation on the transition of bursting phase synchronization of neuronal system under electromagnetic radiation.It is shown that the intensity and frequency of the electric field can induce the transition of the network bursting phase synchronization.Moreover,we also analyze the effect of magnetic flow on the detection of weak signals and stochastic resonance by introducing a subthreshold pacemaker into a single cell of the network and we find that there is an optimal electromagnetic radiation intensity,where the phenomenon of stochastic resonance occurs and the degree of response to the weak signal is maximized.Simulation results show that the extension of the subthreshold pacemaker in the network also depends greatly on coupling strength.The presented results may have important implications for the theoretical study of magnetic stimulation technology,thus promoting further development of transcranial magnetic stimulation（TMS） as an effective means of treating certain neurological diseases.

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 parameterαis 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.

Brain Functional Network Based on Small-Worldness and Minimum Spanning Tree for Depression Analysis

Since the outbreak and spread of corona virus disease 2019(COVID-19),the prevalence of mental disorders,such as depression,has continued to increase.To explore the abnormal changes of brain functional connections in patients with depression,this paper proposes a depression analysis method based on brain function network(BFN).To avoid the volume conductor effect,BFN was constructed based on phase lag index(PLI).Then the indicators closely related to depression were selected from weighted BFN based on small-worldness(SW)characteristics and binarization BFN based on the minimum spanning tree(MST).Differences analysis between groups and correlation analysis between these indicators and diagnostic indicators were performed in turn.The resting state electroencephalogram(EEG)data of 24 patients with depression and 29 healthy controls(HC)was used to verify our proposed method.The results showed that compared with HC,the information processing of BFN in patients with depression decreased,and BFN showed a trend of randomization.

Structural and functional connectivity of the whole brain and subnetworks in individuals with mild traumatic brain injury:predictors of patient prognosis

Patients with mild traumatic brain injury have a diverse clinical presentation,and the underlying pathophysiology remains poorly understood.Magnetic resonance imaging is a non-invasive technique that has been widely utilized to investigate neuro biological markers after mild traumatic brain injury.This approach has emerged as a promising tool for investigating the pathogenesis of mild traumatic brain injury.G raph theory is a quantitative method of analyzing complex networks that has been widely used to study changes in brain structure and function.However,most previous mild traumatic brain injury studies using graph theory have focused on specific populations,with limited exploration of simultaneous abnormalities in structural and functional connectivity.Given that mild traumatic brain injury is the most common type of traumatic brain injury encounte red in clinical practice,further investigation of the patient characteristics and evolution of structural and functional connectivity is critical.In the present study,we explored whether abnormal structural and functional connectivity in the acute phase could serve as indicators of longitudinal changes in imaging data and cognitive function in patients with mild traumatic brain injury.In this longitudinal study,we enrolled 46 patients with mild traumatic brain injury who were assessed within 2 wee ks of injury,as well as 36 healthy controls.Resting-state functional magnetic resonance imaging and diffusion-weighted imaging data were acquired for graph theoretical network analysis.In the acute phase,patients with mild traumatic brain injury demonstrated reduced structural connectivity in the dorsal attention network.More than 3 months of followup data revealed signs of recovery in structural and functional connectivity,as well as cognitive function,in 22 out of the 46 patients.Furthermore,better cognitive function was associated with more efficient networks.Finally,our data indicated that small-worldness in the acute stage could serve as a predictor of longitudinal changes in connectivity in patients with mild traumatic brain injury.These findings highlight the importance of integrating structural and functional connectivity in unde rstanding the occurrence and evolution of mild traumatic brain injury.Additionally,exploratory analysis based on subnetworks could serve a predictive function in the prognosis of patients with mild traumatic brain injury.

Chaos in complex motor networks induced by Newman-Watts small-world connections

We investigate how dynamical behaviours of complex motor networks depend on the Newman-Watts small-world （NWSW） connections. Network elements are described by the permanent magnet synchronous motor （PMSM） with the values of parameters at which each individual PMSM is stable. It is found that with the increase of connection probability p, the motor in networks becomes periodic and falls into chaotic motion as p further increases. These phenomena imply that NWSW connections can induce and enhance chaos in motor networks. The possible mechanism behind the action of NWSW connections is addressed based on stability theory.

Complete and phase synchronization in a heterogeneous small-world neuronal network

Synchronous firing of neurons is thought to be important for information communication in neuronal networks. This paper investigates the complete and phase synchronization in a heterogeneous small-world chaotic Hindmarsh Rose neuronal network. The effects of various network parameters on synchronization behaviour are discussed with some biological explanations. Complete synchronization of small-world neuronal networks is studied theoretically by the master stability function method. It is shown that the coupling strength necessary for complete or phase synchronization decreases with the neuron number, the node degree and the connection density are increased. The effect of heterogeneity of neuronal networks is also considered and it is found that the network heterogeneity has an adverse effect on synchrony.

Small-worldness of brain networks after brachial plexus injury: a resting-state functional magnetic resonance imaging study

Research on brain function after brachial plexus injury focuses on local cortical functional reorganization,and few studies have focused on brain networks after brachial plexus injury.Changes in brain networks may help understanding of brain plasticity at the global level.We hypothesized that topology of the global cerebral resting-state functional network changes after unilateral brachial plexus injury.Thus,in this cross-sectional study,we recruited eight male patients with unilateral brachial plexus injury（right handedness,mean age of 27.9±5.4years old）and eight male healthy controls（right handedness,mean age of 28.6±3.2）.After acquiring and preprocessing resting-state magnetic resonance imaging data,the cerebrum was divided into 90 regions and Pearson’s correlation coefficient calculated between regions.These correlation matrices were then converted into a binary matrix with affixed sparsity values of 0.1–0.46.Under sparsity conditions,both groups satisfied this small-world property.The clustering coefficient was markedly lower,while average shortest path remarkably higher in patients compared with healthy controls.These findings confirm that cerebral functional networks in patients still show smallworld characteristics,which are highly effective in information transmission in the brain,as well as normal controls.Alternatively,varied small-worldness suggests that capacity of information transmission and integration in different brain regions in brachial plexus injury patients is damaged.

Sliding mode synchronization between uncertain Watts-Strogatz small-world spatiotemporal networks

Based on the topological characteristics of small-world networks,a nonlinear sliding mode controller is designed to minimize the effects of internal parameter uncertainties.To qualify the effects of uncertain parameters in the response networks,some effective recognition rates are designed so as to achieve a steady value in the extremely fast simulation time period.Meanwhile,the Fisher-Kolmogorov and Burgers spatiotemporal chaotic systems are selected as the network nodes for constructing a drive and a response network,respectively.The simulation results confirm that the developed sliding mode could realize the effective synchronization problem between the spatiotemporal networks,and the outer synchronization is still achieved timely even when the connection probability of the small-world networks changes.

Controlling bifurcations and chaos in discrete small-world networks

We propose an impulsive hybrid control method to control the period-doubling bifurcations and stabilize unstable periodic orbits embedded in a chaotic attractor of a small-world network. Simulation results show that the bifurcations can be delayed or completely eliminated. A periodic orbit of the system can be controlled to any desired periodic orbit by using this method.

Bifurcations and chaos control in discrete small-world networks

An impulsive delayed feedback control strategy to control period-doubling bifurcations and chaos is proposed. The control method is then applied to a discrete small-world network model. Qualitative analyses and simulations show that under a generic condition, the bifurcations and the chaos can be delayed or eliminated completely. In addition, the periodic orbits embedded in the chaotic attractor can be stabilized.

Small-world networks of neuroblastoma cells cultured in three-dimensional polymeric scaffolds featuring multi-scale roughness

Understanding the mechanisms underlying cell-surface interaction is of fundamental importance for the rational design of scaffolds aiming at tissue engineering,tissue repair and neural regeneration applications.Here,we examined patterns of neuroblastoma cells cultured in three-dimensional polymeric scaffolds obtained by two-photon lithography.Because of the intrinsic resolution of the technique,the micrometric cylinders composing the scaffold have a lateral step size of^200 nm,a surface roughness of around 20 nm,and large values of fractal dimension approaching 2.7.We found that cells in the scaffold assemble into separate groups with many elements per group.After cell wiring,we found that resulting networks exhibit high clustering,small path lengths,and small-world characteristics.These values of the topological characteristics of the network can potentially enhance the quality,quantity and density of information transported in the network compared to equivalent random graphs of the same size.This is one of the first direct observations of cells developing into 3D small-world networks in an artificial matrix.

Evolutionary snowdrift game on heterogeneous Newman-Watts small-world network

We study the evolutionary snowdrift game in a heterogeneous Newman-Watts small-world network. The heterogeneity of the network is controlled by the number of hubs. It is found that the moderate heterogeneity of the network can promote the cooperation best. Besides, we study how the hubs affect the evolution of cooperative behaviours of the heterogeneous Newman-Watts small-world network. Simulation results show that both the initial states of hubs and the connections between hubs can play an important role. Our work gives a further insight into the effect of hubs on the heterogeneous networks.

Study Under AC Stimulation on Excitement Properties of Weighted Small-World Biological Neural Networks with Side-Restrain Mechanism

In this paper, we propose a new model of weighted small-world biological neural networks based on biophysical Hodgkin-Huxley neurons with side-restrain mechanism. Then we study excitement properties of the model under alternating current （AC） stimulation. The study shows that the excitement properties in the networks are preferably consistent with the behavior properties of a brain nervous system under different AC stimuli, such as refractory period and the brain neural excitement response induced by different intensities of noise and coupling. The results of the study have reference worthiness for the brain nerve electrophysiology and epistemological science.

Optimal network structure to induce the maximal small-world effect

In this paper, the general efficiency, which is the average of the global efficiency and the local efficiency, is defined to measure the communication efficiency of a network. The increasing ratio of the general efficiency of a small-world network relative to that of the corresponding regular network is used to measure the small-world effect quantitatively. The more considerable the small-world effect, the higher the general efficiency of a network with a certain cost is. It is shown that the small-world effect increases monotonically with the increase of the vertex number. The optimal rewiring probability to induce the best small-world effect is approximately 0.02 and the optimal average connection probability decreases monotonically with the increase of the vertex number. Therefore, the optimal network structure to induce the maximal small-world effect is the structure with the large vertex number （〉 500）, the small rewiring probability （≈0.02） and the small average connection probability （〈 0.1）. Many previous research results support our results.

Dynamics of organizational rumor communication on connecting multi-small-world networks

We study the dynamics of an epidemic-like model for the spread of a rumor on a connecting multi-small-world- network （CM-SWN） model, which represents organizational communication in the real world. It has been shown that this model exhibits a transition between regimes of localization and propagation at a finite value of network randomness. Here, by numerical means, we perform a quantitative characterization of the evolution in the three groups under two evolution rules, namely the conformity and obeying principles. The variant of a dynamic CM-SWN, where the quenched disorder of small-world networks is replaced by randomly changing connections between individuals in a single network and stable connection by star nodes between networks, is also analysed in detail and compared with a mean-field approximation.

Plasticity-induced characteristic changes of pattern dynamics and the related phase transitions in small-world neuronal networks

Phase transitions widely exist in nature and occur when some control parameters are changed. In neural systems, their macroscopic states are represented by the activity states of neuron populations, and phase transitions between different activity states are closely related to corresponding functions in the brain. In particular, phase transitions to some rhythmic synchronous firing states play significant roles on diverse brain functions and disfunctions, such as encoding rhythmical external stimuli, epileptic seizure, etc. However, in previous studies, phase transitions in neuronal networks are almost driven by network parameters （e.g., external stimuli）, and there has been no investigation about the transitions between typical activity states of neuronal networks in a self-organized way by applying plastic connection weights. In this paper, we discuss phase transitions in electrically coupled and lattice-based small-world neuronal networks （LBSW networks） under spike-timing-dependent plasticity （STDP）. By applying STDP on all electrical synapses, various known and novel phase transitions could emerge in LBSW networks, particularly, the phenomenon of self-organized phase transitions （SOPTs）： repeated transitions between synchronous and asynchronous firing states. We further explore the mechanics generating SOPTs on the basis of synaptic weight dynamics.

Local Interactions and the Emergence of a Twitter Small-World Network

The small-world phenomenon is found in many self-organising systems. Systems configured in small-world networks spread information more easily than in random or regular lattice-type networks. Whilst it is a known fact that small-world networks have short average path length and high clustering coefficient in self-organising systems, the ego centralities that maintain the cohesiveness of small-world network have not been formally defined. Here we show that instantaneous events such as the release of news items via Twitter, coupled with active community arguments related to the news item form a particular type of small-world network. Analysis of the centralities in the network reveals that community arguments maintain the small-world network whilst ac-tively maintaining the cohesiveness and boundary of the group. The results demonstrate how an active Twitter community unconsciously forms a small-world network whilst interacting locally with a bordering community. Over time, such local interactions brought about the global emergence of the small-world network, connecting media channels with human activities. Understanding the small-world phenomenon in relation to online social or civic movement is important, as evident in the spate of online activists that tipped the power of governments for the better or worst in recent times. The support, or removal of high centrality nodes in such networks has important ramifications in the self-expression of society and civic discourses. The presentation in this article anticipates further exploration of man-made self-organising systems where a larger cluster of adhoc and active community maintains the overall cohesiveness of the network.

An effective method to improve the robustness of small-world networks under attack

In this study, the robustness of small-world networks to three types of attack is investigated. Global efficiency is introduced as the network coefficient to measure the robustness of a small-world network. The simulation results prove that an increase in rewiring probability or average degree can enhance the robustness of the small-world network under all three types of attack. The effectiveness of simultaneously increasing both rewiring probability and average degree is also studied, and the combined increase is found to significantly improve the robustness of the small-world network. Furthermore, the combined effect of rewiring probability and average degree on network robustness is shown to be several times greater than that of rewiring probability or average degree individually. This means that small-world networks with a relatively high rewiring probability and average degree have advantages both in network communications and in good robustness to attacks. Therefore, simultaneously increasing rewiring probability and average degree is an effective method of constructing realistic networks. Consequently, the proposed method is useful to construct efficient and robust networks in a realistic scenario.

Model for Generating Scale-Free Artificial Social Networks Using Small-World Networks

The Internet of Things(IoT)has the potential to be applied to social networks due to innovative characteristics and sophisticated solutions that challenge traditional uses.Social network analysis(SNA)is a good example that has recently gained a lot of scientific attention.It has its roots in social and economic research,as well as the evaluation of network science,such as graph theory.Scientists in this area have subverted predefined theories,offering revolutionary ones regarding interconnected networks,and they have highlighted the mystery of six degrees of separation with confirmation of the small-world phenomenon.The motivation of this study is to understand and capture the clustering properties of large networks and social networks.We present a network growth model in this paper and build a scale-free artificial social network with controllable clustering coefficients.The random walk technique is paired with a triangle generating scheme in our proposed model.As a result,the clustering controlmechanism and preferential attachment(PA)have been realized.This research builds on the present random walk model.We took numerous measurements for validation,including degree behavior and the measure of clustering decay in terms of node degree,among other things.Finally,we conclude that our suggested random walk model is more efficient and accurate than previous state-of-the-art methods,and hence it could be a viable alternative for societal evolution.

Nonlinear Dynamical Behavior in BS Evolution Model Based on Small-World Network Added with Nonlinear Preference

We introduce a modified small-world network adding new links with nonlinearly preferential connectioninstead of adding randomly,then we apply Bak-Sneppen(BS)evolution model on this network.We study severalimportant structural properties of our network such as the distribution of link-degree,the maximum link-degree,and thegth of the shortest path.We further argue several dynamical characteristics of the model such as the important criticalvalue f_c,the f_0 avalanche,and the mutating condition,and find that those characteristics show panticular behaviors.