Impact of small-world topologies on broadcasting for wireless sensor networks

Broadcasting is an important operation and been widely used in wireless sensor networks （WSNs）. These networks are power constrained as nodes operate with limited battery power. Wireless sensor networks are spatial graphs that have much more clustered and much high path-length characteristics. After considering energy- efficient broadcasting in such networks, by combining the small-world characteristic of WSNs and the properties of ant algorithm to quickly identify an optimal path, small-world power-aware broadcast algorithm is introduced and evaluated. Given different densities of network, simulation results show that our algorithm significantly improves life of networks and also reduces communication distances and power consumption.

Immunizations on small worlds of tree-based wireless sensor networks

The sensor virus is a serious threat,as an attacker can simply send a single packet to compromise the entire sensor network.Epidemics become drastic with link additions among sensors when the small world phenomena occur.Two immunization strategies,uniform immunization and temporary immunization,are conducted on small worlds of tree-based wireless sensor networks to combat the sensor viruses.With the former strategy,the infection extends exponentially,although the immunization effectively reduces the contagion speed.With the latter strategy,recurrent contagion oscillations occur in the small world when the spatial-temporal dynamics of the epidemic are considered.The oscillations come from the small-world structure and the temporary immunization.Mathematical analyses on the small world of the Cayley tree are presented to reveal the epidemic dynamics with the two immunization strategies.

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.

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.

Self-Organized Criticality in Small-World Networks Based on the Social Balance Dynamics

A node model is proposed to study the self-organized criticality in the small-world networks which represent the social networks.Based on the node model and the social balance dynamics,the social networks are mapped to the thermodynamic systems and the phenomena are studied with physical methods.It is found that the avalanche in the small-world networks at the critical state satisfies the power-law distribution spatially and temporally.

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.

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.

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.

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.

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.

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.

Dynamics in small worlds of tree topologies of wireless sensor networks

Tree topologies, which construct spatial graphs with large characteristic path lengths and small clustering coefficients, are ubiquitous in deployments of wireless sensor networks. Small worlds are investigated in tree-based networks. Due to link ad- ditions, characteristic path lengths reduce rapidly and clustering coefficients increase greatly. A tree abstract, Cayley tree, is con- sidered for the study of the navigation algorithm, which runs auto- matically in the small worlds of tree-based networks. In the further study, epidemics in the small worlds of tree-based wireless sen- sor networks on the large scale are studied, and the percolation threshold is calculated, at which the outbreak of the epidemic takes place. Compared with Cayley tree, there is a smaller percolation threshold suffering from the epidemic.

Outer synchronization of uncertain small-world networks via adaptive sliding mode control

The outer synchronization of irregular coupled complex networks is inves- tigated with nonidentical topological structures. The switching gain is estimated by an adaptive technique, and a sliding mode controller is designed to satisfy the sliding con- dition. The outer synchronization between two irregular coupled complex networks with different initial conditions is implemented via the designed controllers with the corre- sponding parameter update laws. The chaos synchronization of two small-world networks consisting of N uncertain identical Lorenz systems is achieved to demonstrate the appli- cations of the proposed approach.

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.

Small World Effects in a Harmonious Unifying Hybrid Preferential Model Networks

Small worm effects in the harmonious unifying hybrid preferential model （HUHPM） networks are studied both numerically and analytically. The idea and method of the HUHPM is applied to three typical examples of unweighted BA model, weighted BBV model, and the TDE rnodel, so-called HUHPM-BA, HUHPM-BBV and HUHPM- TDE networks. Comparing the HUHPM with current typical models above, it is found that the HUHPM networks has the smallest average path length and the biggest average clustering coefficient. The results demonstrate that the HUHPM is more suitable not only for the un-iveighted models but also for the weighted models.

Comparison of Ising Model and Potts Model on Non-Local Directed Small-World Networks

Further to the investigation of the critical properties of the Potts model with q = 3 and 8 states in one dimension (1D) on directed small-world networks reported by Aquino and Lima, which presents, in fact, a second-order phase transition with a new set of critical exponents, in addition to what was reported in Sumour and Lima in studying Ising model on non-local directed small-world for several values of probability 0 < P < 1. In this paper the behavior of two models discussed previously, will be re-examined to study differences between their behavior on directed small-world networks for networks of different values of probability P = 0.1, 0.2, 0.3, 0.4 and 0.5 with different lattice sizes L = 10, 20, 30, 40, and 50 to compare between the important physical variables between Ising and Potts models on the directed small-world networks. We found in our paper that is a phase transitions in both Ising and Potts models depending essentially on the probability P.