Nonlinear Dynamical Behavior in Neuron Model Based on Small World Network with Attack and Repair Strategy

In this paper, we investigate the effect due to the change of topology structure of network on the nonlinear dynamical behavior, by virtue of the OFC neuron evolution model with attack and repair strategy based on the small world. In particular, roles of various parameters relating to the dynamical behavior are carefully studied and analyzed. In addition, the avalanche and EEC-like wave activities with attack and repair strategy are also explored in detail in this work.

A Modified Earthquake Model of Self-Organized Criticality on Small World Networks

A modified Olami Feder-Christensen model of self-organized criticality on a square lattice with the properties of small world networks has been studied.We find that our model displays power-law behavior and the exponent τ of the model depends on φ,the density of long-range connections in our network.

Complex Behavior in a Selective Aging Neuron Model Based on Small World Networks

Complex behavior in a selective aging simple neuron model based on small world networks is investigated. The basic elements of the model are endowed with the main features of a neuron function. The structure of the selective aging neuron model is discussed. We also give some properties of the new network and find that the neuron model displays a power-law behavior. If the brain network is small world-like network, the mean avalanche size is almost the same unless the aging parameter is big enough.

Self-organized Criticality and Synchronization in a Pulse-coupled Integrate-and-Fire Neuron Model Based on Small World Networks＊

A lattice model for a set of pulse-coupled integrate-and-fire neurons with small world structure is introduced.We find that our model displays the power-law behavior accompanied with the large-scale synchronized activities among the units. And the different connectivity topologies lead to different behaviors in models of integrate-and-fire neurons.

Effects of Aging and Self-organized Criticality in a Pulse-Coupled Integrate-and-Fire Neuron Model Based on Small World Networks

Effects of aging and self-organized criticality in a pulse-coupled integrate-and-fire neuron model based on small world networks have been studied. We give the degree distribution of aging network, average shortest path length, the diameter of our network, and the clustering coefficient, and find that our neuron model displays the power-law behavior, and with the number of added links increasing, the effects of aging become smaller and smaller. This shows that if the brain works at the self-organized criticality state, it can relieve some effects caused by aging.

Effects of Different Connectivity Topologies in Small World Networks on EEG-Like Activities

Based on our previously pulse-coupled integrate-and-fire neuron model in small world networks, we investigate the effects of different connectivity topologies on complex behavior of electroencephalographic-like signals produced by this model. We show that several times series analysis methods that are often used for analyzing complex behavior of electroencephalographic-like signals, such as reconstruction of the phase space, correlation dimension, fractal dimension, and the Hurst exponent within the rescaled range analysis （R/S）. We lind that the different connectivity topologies lead to different dynamical behaviors in models of integrate-and-fire neurons.

SEIR-SW, Simulation Model of Influenza Spread Based on the Small World Network

This study modeled the spread of an influenza epidemic in the population of Oran, Algeria. We investigated the mathematical epidemic model, SEIR（Susceptible-Exposed-Infected-Removed）, through extensive simulations of the effects of social network on epidemic spread in a Small World（SW） network, to understand how an influenza epidemic spreads through a human population. A combined SEIR-SW model was built, to help understand the dynamics of infectious disease in a community, and to identify the main characteristics of epidemic transmission and its evolution over time. The model was also used to examine social network effects to better understand the topological structure of social contact and the impact of its properties. Experiments were conducted to evaluate the combined SEIR-SW model. Simulation results were analyzed to explore how network evolution influences the spread of desease, and statistical tests were applied to validate the model. The model accurately replicated the dynamic behavior of the real influenza epidemic data, confirming that the susceptible size and topological structure of social networks in a human population significantly influence the spread of infectious diseases. Our model can provide health policy decision makers with a better understanding of epidemic spread,allowing them to implement control measures. It also provides an early warning of the emergence of influenza epidemics.

Order parameters and synchronization of FitzHugh-Nagumo small-world networks

This paper numerically investigates the order parameter and synchronisation in the small world connected FitzHugh-Nagumo excitable systems. The simulations show that the order parameter continuously decreases with increasing D, the quality of the synchronisation worsens for large noise intensity. As the coupling intensity goes up, the quality of the synchronisation worsens, and it finds that the larger rewiring probability becomes the larger order parameter. It obtains the complete phase diagram for a wide range of values of noise intensity D and control parameter g.

Integration of small world networks with multi-agent systems for simulating epidemic spatiotemporal transmission

This study proposes an integrated model based on small world network (SWN) and multi-agent system (MAS) for simulating epidemic spatiotemporal transmission. In this model, MAS represents the process of spatiotemporal interactions among individuals, and SWN describes the social relation network among agents. The model is composed of agent attribute definitions, agent movement rules, neighborhoods, construction of social relation network among agents and state transition rules. The construction of social relation network and agent state transition rules is essential for implementing the proposed model. The decay effects of infection "memory", distance and social relation between agents are introduced into the model, which are unavailable in traditional models. The proposed model is used to simulate the transmission process of flu in Guangzhou City based on the swarm software platform. The integration model has better performance than the traditional SEIR model and the pure MAS based epidemic model. This model has been applied to the simulation of the transmission of epidemics in real geographical environment. The simulation can provide useful information for the understanding, prediction and control of the transmission of epidemics.

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.

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.

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.

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.

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.

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.

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.

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.

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.