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.

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.

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 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.

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.

Small World Properties Generated by a New Algorithm Under Same Degree of All Nodes

Based on the model of the same degree of all nodes we proposed before, a new algorithm, the so-called “spread all over vertices” （SAV） algorithm, is proposed for generating small-world properties from a regular ring lattices. During randomly rewiring connections the SAV is used to keep the unchanged number of links. Comparing the SAV algorithm with the Watts-Strogatz model and the “spread all over boundaries” algorithm, three methods can have the same topological properties of the small world networks. These results offer diverse formation of small world networks. It is helpful to the research of some applications for dynamics of mutual oscillator inside nodes and interacting automata associated with networks.

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.

Analysis of Commuting Modal Shift in Consideration of Social Interaction of Consciousness for Environment

It is the matter for achievement of the low carbon transport system that the excessive use of private vehicles can be controlled appropriately.Not only improvement of service level of modes except private vehicle,but also consciousness for environmental problem of individual trip maker is important for eco-commuting promotion.On the other hand,consciousness for environment would be changed by influence of other person.Accordingly,it is aimed in the study that the structure of decision-making process for modal shift to the eco-commuting mode in the local city is described considering environmental consciousness and social interaction.For the purpose,the consciousness for the environment problem and the travel behavior of the commuter at the suburban area in the local city are investigated by the questionnaire survey.The covariance structure about the eco-consciousness is analyzed with the database of the questionnaire survey by structural equation modeling.As the result,it can be confirmed with the structural equation model that the individual environmental consciousness is strongly related with the intention of self-sacrifice and is influenced with the local interaction of the individual connections.On the other hand,the intention of modal shift for the commuting mode is analyzed with the database of the questionnaire survey.It can be found out that the environmental consciousness is not statistically significant for commuting mode choice with the present poor level of service of public transport.However,the intention of self-sacrifice for the prevention of the global warming is statistically confirmed as the factor of modal shift with the operation of eco-commuting bus service with the RP/SP integrated estimation method.As the result,the multi-agent simulation system with social interaction model for eco consciousness is developed to measure the effect of the eco-commuting promotion.For the purpose,the carbon dioxide emission is estimated based on traffic demand and road network condition in the traffic environment model.On the other hand,the relation between agents is defined based on the small world network.The proposed multi-agent simulation is applied to measure the effect of the eco-commuting promotion such as improvement of level of service on the public transport or education of eco-consciousness.The effect of the promotion plan can be observed with the proposed multi-agent system.Finally,it can be concluded that the proposed multi-agent simulation with social interaction for eco-consciousness is useful for planning of eco-commuting promotion.

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.

Orientation in Social Networks

Stanley Milgram's small world experiment presents "six degrees of separation" of our world.One phenomenon of the experiment still puzzling us is that how individuals operating with the social network information with their characteristics can be very adept at finding the short chains. The previous works on this issue focus whether on the methods of navigation in a given network structure,or on the effects of additional information to the searching process. In this paper, the authors emphasize that the growth and shape of network architecture is tightly related to the individuals' attributes. The authors introduce a method to reconstruct nodes' intimacy degree based on local interaction. Then we provide an intimacy based approach for orientation in networks. The authors find that the basic reason of efficient search in social networks is that the degree of "intimacy" of each pair of nodes decays with the length of their shortest path exponentially. Meanwhile, the model can explain the hubs limitation which was observed in real-world experiment.

Exploration of unpredictable environments by networked groups

Information sharing is a critical task for group-living animals. The pattern of sharing can be modeled as a network whose structure can affect the decision-making performance of individual members as well as that of the group as a whole. A fully connected network, in which each member can directly transfer information to all other members, ensures rapid sharing of important information, such as a promising foraging location. However, it can also impose costs by amplifying the spread of inaccur- ate information （if, for example the foraging location is actually not profitable）. Thus, an optimal net- work structure should balance effective sharing of current knowledge with opportunities to discover new information. We used a computer simulation to measure how well groups characterized by dif- ferent network structures （fully connected, small world, lattice, and random） find and exploit resource peaks in a variable environment. We found that a fully connected network outperformed other struc- tures when resource quality was predictable. When resource quality showed random variation, however, the small world network was better than the fully connected one at avoiding extremely poor outcomes. These results suggest that animal groups may benefit by adjusting their informa- tion-sharing network structures depending on the noisiness of their environment.