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.     

Internal degrees of freedom, long-range interactions and nonlocal effects in perturbed Klein-Gordon equations

We investigate different mechanisms for the excitation of soliton internal degrees of freedom and for the existence of long-range interactions between solitons. We will study a nonlocal Klein-Gordon equation that is used as a model for Josephson junctions in thin films. We will show the connections between nonlocality, nonlinearity, internal degrees of freedom, long-range interactions and power-law behaviors.     

Spatial and Temporal Behaviors in a Modified Evolution Model Based on Small World Network

In this paper, we introduce a new modified evolution model on a small world network. In our model,the spatial and temporal correlations and the spatial-temporal evolve pattern of mutating nodes exhibit some particular behaviors different from those of the original BS evolution model. More importantly, these behaviors will change with φ, the density of short paths in our network.     

Multifractal Detrended Fluctuation Analysis of Interevent Time Series in a Modified OFC Model

We use multifractal detrended fluctuation analysis(MF-DFA) method to investigate the multifractal behavior of the interevent time series in a modified Olami-Feder-Christensen(OFC) earthquake model on assortative scale-free networks.We determine generalized Hurst exponent and singularity spectrum and find that these fluctuations have multifractal nature.Comparing the MF-DFA results for the original interevent time series with those for shuffled and surrogate series,we conclude that the origin of multifractality is due to both the broadness of probability density function and long-range correlation.     

Complex Behavior in an Integrate-and-Fire Neuron Model Based on Small World Networks

Based on our previously pulse-coupled integrate-and-fire neuron model in small world networks, we investigate the complex behavior of electroencephalographic (EEG)-like activities produced by such a model. We find EEG-like activities have obvious chaotic characteristics. We also analyze the complex behaviors of EEG-like signals,such as spectral analysis, reconstruction of the phase space, the correlation dimension, and so on.     

Flat-head power-law, size-independent clustering, and scaling of coevolutionary scale-free networks

Scale-free topology and high clustering coexist in some real networks, and keep invariant for growing sizes of the systems. Previous models could hardly give out size-independent clustering with selforganized mechanism when succeeded in producing power-law degree distributions. Always ignored, some empirical statistic results display flat-head power-law behaviors. We modify our recent coevolutionary model to explain such phenomena with the inert property of nodes to retain small portion of unfavorable links in self-organized rewiring process. Flat-head power-law and size-independent clustering are induced as the new characteristics by this modification. In addition, a new scaling relation is found as the result of interplay between node state growth and adaptive variation of connections.     

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.     

Self-Organized Criticality Analysis of Earthquake Model Based on Heterogeneous Networks

The original Olami-Feder-Christensen (OFC) model, which displays a robust power-law behavior, is a quasistatic two-dimensional version of the Burridge--Knopoff spring-block model of earthquakes. In this paper, we introduce a modified OFC model based on heterogeneous network, improving the redistribution rule of the original model. It can be seen as a generalization of the original OFC model. We numerically investigate the influence of theparameters θ and β, which respectively control the intensity of the evolutivemechanism of the topological growth and the inner selection dynamicsin our networks, and find that there are two distinct phases in theparameter space (θ, β). Meanwhile, we study the influence of the control parameter a either. Increasing a, the earthquake behavior of the model transfers from local to global.     

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.     

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 find that the different connectivity topologies lead to different dynamical behaviors in models of integrate-and-fire neurons.     

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.     

Olami-Feder-Christensen model on different networks

We investigate numerically the Self Organized Criticality (SOC) properties of the dissipative Olami-Feder-Christensen model on small-world and scale-free networks. We find that the small-world OFC model exhibits self-organized criticality. Indeed, in this case we observe power law behavior of earthquakes size distribution with finite size scaling for the cut-off region. In the scale-free OFC model, instead, the strength of disorder hinders synchronization and does not allow to reach a critical state.     

Analysis of self-organized criticality in weighted coupled systems

A weighted Olami, Feder, and Christensen (OFC) model, improving the redistribution rule of the original model, has been introduced. It can be seen as a generalization of the OFC model and exhibits Self-organized criticality (SOC) behavior, too. The stress evolution process has been accelerated and the nontrivial relationship between the exponent of 1/f and the control parameter has been reported. Although our model is simple, we obtained more reasonable avalanche dimensions than with the previous model.     

Criticality in Two-Variable Earthquake Model on a Random Graph

A two-variable earthquake model on a quenched random graph is established here. It can be seen as a generalization of the OFC models. We numerically study the critical behavior of the model when the system is nonconservative: the result indicates that the model exhibits self-organized criticality deep within the nonconservative regime. The probability distribution for avalanche size obeys finite size scaling. We compare our model with the model introduced by Stefano Lise and Maya Paczuski [Phys. Rev. Lett. 88 (2002) 228301], it is proved that they are not in the same universality class.     

Dynamical network interactions in distributed control of robots

In this paper the dynamical network model of the interactions within a group of mobile robots is investigated and proposed as a possible strategy for controlling the robots without central coordination. Motivated by the results of the analysis of our simple model, we show that the system performance in the presence of noise can be improved by including long-range connections between the robots. Finally, a suitable strategy based on this model to control exploration and transport is introduced.     

相互作用herding模型:记忆与遗忘

相互作用herding 模型仅考虑上一事件对当前经济活动的影响，实际经济活动中经纪人对过去的经济活动是具有深度记忆的，过去各个事件对当前经济活动都应该有影响，但是由于遗忘，它们的影响又各不相同.具有长程记忆的相互作用herding模型认为过去各个事件对当前经济活动的影响随时间是呈指数衰退的，它不仅体现经纪人对历史具有深度的记忆能力，同时也反映出人的遗忘本性.数值计算表明，该模型不仅能重现相互作用herding模型的动力学特性，并且较好地反映真实的经济行为. 关键词： 记忆 遗忘 相互作用herding模型 指数衰退     

Precursory phenomena associated with large avalanches in the long-range connective sandpile (LRCS) model

Reduction in b-values before a large earthquake is a very popular topic for discussion. This study proposes an alternative sandpile model being able to demonstrate reduction in scaling exponents before large events through adaptable long-range connections. The distant connection between two separated cells was introduced in the sandpile model. We found that our modified long-range connective sandpile (LRCS) system repeatedly approaches and retreats from a critical state. When a large avalanche occurs in the LRCS model, accumulated energy dramatically dissipates and the system simultaneously retreats from criticality. The system quickly approaches the critical state accompanied by the increase in the slopes of the power-law frequency-size distributions of events. Afterwards, and most interestingly, the power-law slope declines before the next large event. The precursory b-value reduction before large earthquakes observed from earthquake catalogues closely mimics the evolution in power-law slopes for the frequency-size distributions of events derived in the LRCS models. Our paper, thus, provides a new explanation for declined b-values before large earthquakes.     

电子商务中人类活动的标度行为实证研究

应用去趋势波动分析法,对电子商务中人类网上购物行为进行研究,首次探讨了人类浏览及购买行为时间序列(数量波动)标度律.首先,研究发现人类网上购物行为呈现出明显的周期性,其时间序列的概率密度函数具有显著的双模态特征.其次,利用傅里叶变换方法分析浏览以及购买行为时间序列的功率谱,发现其演化过程不同于无关联的泊松过程.最后,基于功率谱过滤周期性趋势的影响,对去除周期趋势后的浏览和购买行为时间序列进行去趋势波动分析,发现其标度行为表明其具有较强的长程关联特性,且平均标度值近似为1,表明其具有自组织临界性.实证研究结果与其他领域如因特网交通流和金融市场价格波动的标度行为相似,有助于理解人类活动如何影响电子商务系统演化和提高在线商务活动效率,对分析电子商务中人类行为活动的机制和预测其波动趋势具有重要的启示作用.     

Modeling Topology and Nonlinear Dynamical Behavior of the Weighted Scale-Free Networks

An improved weighted scale-free network, which has two evolution mechanisms: topological growth and strength dynamics, has been introduced. The topology structure of the model will be explored in details in this work. The evolution driven mechanism of Olami-Feder-Christensen (OFC) model is added to our model to study the self-organized criticality and the dynamical behavior. We also consider attack mechanism and the study of the model with attack is also investigated in this paper. We find there are differences between the model with attack and without attack.     

Epidemic Spread in Networks Induced by Deactivation Mechanism

We have studied the topology and epidemic spreading behaviors on the networks in which deactivation mechanism and long-rang connection are coexisted. By means of numerical simulation, we find that the clustering coefficient C and the Pearson correlation coefficient r decrease with increasing long-range connection μ and the topological state of the network changes into that of BA model at the end （when μ = 1）. For the Susceptible-Infect-Susceptible model of epidemics, the epidemic threshold can reach maximum value at μ = 0.4 and presents two different variable states around μ= 0.4.