复杂系统的Scale-free性及其宏观调控问题

系统研究了复杂系统的Scale-free问题,包括复杂系统的Scale-free性、幂律分布的分析、Scale-free性的形成机制、复杂系统的Scale-free现象,以及复杂系统Scale-free性的宏观调控等问题。研究结果强调:(1)从广义上说,Scale-free性是描述大量复杂系统整体上严重不均匀分布的一种内在性质;(2)证明了只有当幂律指数在2～3之间时,用幂律分布所描述的大量复杂系统才具有严重的不均匀分布特性;(3)对于国计民生有重大影响的复杂系统,提出了Scale-free性的宏观调控的原则方法。

Generation of scale-free knowledge network with local world mechanism

In order to simulate the real growing process, a new type of knowledge network growth mechanism based on local world connectivity is constructed. By the mean-field method, theoretical prediction of the degree distribution of the knowledge network is given, which is verified by Matlab simulations. When the new added node＇s local world size is very small, the degree distribution of the knowledge network approximately has the property of scale-free. When the new added node＇s local world size is not very small, the degree distribution transforms from pure power-law to the power-law with an exponential tailing. And the scale-free index increases as the number of new added edges decreases and the tunable parameters increase. Finally, comparisons of some knowledge indices in knowledge networks generated by the local world mechanism and the global mechanism are given. In the long run, compared with the global mechanism, the local world mechanism leads the average knowledge levels to slower growth and brings homogenous phenomena.

基于组增长的小世界Scale-free网络模型

小世界和Scale-free是很多大规模复杂网络的重要特征,建立体现这些特征的网络模型是研究网络结构和行为的重要基础。针对现有模型不能全面地反映实际网络所具有的特征属性,提出了基于组增长的小世界 Scale-free网络模型。该模型在小世界和 Scale-free模型的基础上,结合了节点的本地强连接性、新增连接的度相关性和网络动态的增长方式,把小世界和 Scale-free联系了起来。仿真结果表明,该模型生成的网络图同时具有小世界和 Scale-free特征。

Immunization for scale-free networks by random walker

Based on the random walk and the intentional random walk, we propose two types of immunization strategies which require only local connectivity information. On several typical scale-free networks, we demonstrate that these strategies can lead to the eradication of the epidemic by immunizing a small fraction of the nodes in the networks. Particularly, the immunization strategy based on the intentional random walk is extremely efficient for the assortatively mixed networks.

Improving Dendritic Neuron Model With Dynamic Scale-Free Network-Based Differential Evolution

Some recent research reports that a dendritic neuron model(DNM)can achieve better performance than traditional artificial neuron networks(ANNs)on classification,prediction,and other problems when its parameters are well-tuned by a learning algorithm.However,the back-propagation algorithm(BP),as a mostly used learning algorithm,intrinsically suffers from defects of slow convergence and easily dropping into local minima.Therefore,more and more research adopts non-BP learning algorithms to train ANNs.In this paper,a dynamic scale-free network-based differential evolution(DSNDE)is developed by considering the demands of convergent speed and the ability to jump out of local minima.The performance of a DSNDE trained DNM is tested on 14 benchmark datasets and a photovoltaic power forecasting problem.Nine meta-heuristic algorithms are applied into comparison,including the champion of the 2017 IEEE Congress on Evolutionary Computation(CEC2017)benchmark competition effective butterfly optimizer with covariance matrix adapted retreat phase(EBOwithCMAR).The experimental results reveal that DSNDE achieves better performance than its peers.

Phase transition in evolution of traffic flow with scale-free property

This paper investigates the behaviour of traffic flow in traffic systems with a new model based on the NaSch model and cluster approximation of mean-field theory. The proposed model aims at constructing a mapping relationship between the microcosmic behaviour and the macroscopic property of traffic flow. Results demonstrate that scale-free phenomenon of the evolution network becomes obvious when the density value of traffic flow reaches at the critical point of phase transition from free flow to traffic congestion, and jamming is limited in this scale-free structure.

Epidemic spreading in scale-free networks including the effect of individual vigilance

In this paper, we study the epidemic spreading in scale-flee networks and propose a new susceptible-infected- recovered （SIR） model that includes the effect of individual vigilance. In our model, the effective spreading rate is dynamically adjusted with the time evolution at the vigilance period. Using the mean-field theory, an analytical result is derived. It shows that individual vigilance has no effect on the epidemic threshold. The numerical simulations agree well with the analytical result. Purthermore, we investigate the effect of individual vigilance on the epidemic spreading speed. It is shown that individual vigilance can slow the epidemic spreading speed effectively and delay the arrival of peak epidemic infection.

Cascading failure in the wireless sensor scale-free networks

In the practical wireless sensor networks （WSNs）, the cascading failure caused by a failure node has serious impact on the network performance. In this paper, we deeply research the cascading failure of scale-free topology in WSNs. Firstly, a cascading failure model for scale-free topology in WSNs is studied. Through analyzing the influence of the node load on cascading failure, the critical load triggering large-scale cascading failure is obtained. Then based on the critical load, a control method for cascading failure is presented. In addition, the simulation experiments are performed to validate the effectiveness of the control method. The results show that the control method can effectively prevent cascading failure.

Malicious Code Modeling and Analysis in Weighted Scale-Free Networks

We study the detailed malicious code propagating process in scale-free networks with link weights that denotes traffic between two nodes. It is found that the propagating velocity reaches a peak rapidly then decays in a power-law form, which is different from the well-known result in unweighted network case. Simulation results show that the nodes with larger strength are preferential to be infected, but the hierarchical dynamics are not clearly found. The simulation results also show that larger dispersion of weight of networks leads to slower propagating, which indicates that malicious code propagates more quickly in unweighted scale-free networks than in weighted scale-free networks under the same condition. These results show that not only the topology of networks but also the link weights affect the malicious propagating process.

Degree distribution and robustness of cooperative communication network with scale-free model

With the requirements of users enhanced for wireless communication, the cooperative communication will become a development trend in future. In this paper, a model based on complex networks with both preferential attachment is researched to solve an actual network CCN （Cooperative Communication Network）. Firstly, the evolution of CCN is given by four steps with different probabilities. At the same time, the rate equations of nodes degree are presented to analyze the evolution of CCN. Secondly, the degree distribution is analyzed by calculating the rate equation and numerical simulation. Finally, the robustness of CCN is studied by numerical simulation with random attack and intentional attack to analyze the effects of degree distribution and average path length. The results of this paper are more significant for building CCN to programme the resource of communication.

Epidemic spreading on a scale-free network with awareness

This paper presents a modified susceptible-infected-recovered（SIR） model with the effects of awareness and vaccination to study the epidemic spreading on scale-free networks based on the mean-field theory.In this model,when susceptible individuals receive awareness from their infected neighbor nodes,they will take vaccination measures.The theoretical analysis and the numerical simulations show that the existence of awareness and vaccination can significantly improve the epidemic threshold and reduce the risk of virus outbreaks.In addition,regardless of the existence of vaccination,the awareness can increase the spreading threshold and slow the spreading speed effectively.For a given awareness and a certain spreading rate,the total number of infections reduces with the increasing vaccination rate.

A novel evolving scale-free model with tunable attractiveness

In this paper, a new evolving model with tunable attractiveness is presented. Based on the Barabasi-Albert （BA） model, we introduce the attractiveness of node which can change with node degree. Using the mean-field theory, we obtain the analytical expression of power-law degree distribution with the exponent γ∈ （3, ∞）. The new model is more homogeneous and has a lower clustering coefficient and bigger average path length than the BA model.

Adaptive local routing strategy on a scale-free network

Due to the heterogeneity of the structure on a scale-free network, making the betweennesses of all nodes become homogeneous by reassigning the weights of nodes or edges is very difficult. In order to take advantage of the important effect of high degree nodes on the shortest path communication and preferentially deliver packets by them to increase the probability to destination, an adaptive local routing strategy on a scale-free network is proposed, in which the node adjusts the forwarding probability with the dynamical traffic load （packet queue length） and the degree distribution of neighbouring nodes. The critical queue length of a node is set to be proportional to its degree, and the node with high degree has a larger critical queue length to store and forward more packets. When the queue length of a high degree node is shorter than its critical queue length, it has a higher probability to forward packets. After higher degree nodes are saturated （whose queue lengths are longer than their critical queue lengths）, more packets will be delivered by the lower degree nodes around them. The adaptive local routing strategy increases the probability of a packet finding its destination quickly, and improves the transmission capacity on the scale-free network by reducing routing hops. The simulation results show that the transmission capacity of the adaptive local routing strategy is larger than that of three previous local routing strategies.

Effects of channel noise on synchronization transitions in delayed scale-free network of stochastic Hodgkin–Huxley neurons

We numerically study the effect of the channel noise on the spiking synchronization of a scale-free Hodgkin-Huxley neuron network with time delays. It is found that the time delay can induce synchronization transitions at an intermediate and proper channel noise intensity, and the synchronization transitions become strongest when the channel noise intensity is optimal. The neurons can also exhibit synchronization transitions as the channel noise intensity is varied, and this phenomenon is enhanced at around the time delays that can induce the synchronization transitions. It is also found that the synchronization transitions induced by the channel noise are dependent on the coupling strength and the network average degree, and there is an optimal coupling strength or network average degree with which the synchronization transitions become strongest. These results show that by inducing synchronization transitions, the channel noise has a big regulation effect on the synchronization of the neuronal network. These findings could find potential implications for the information transmission in neural systems.

Mobile user forecast and power-law acceleration invariance of scale-free networks

This paper studies and predicts the number growth of China＇s mobile users by using the power-law regression. We find that the number growth of the mobile users follows a power law. Motivated by the data on the evolution of the mobile users, we consider scenarios of self-organization of accelerating growth networks into scale-free structures and propose a directed network model, in which the nodes grow following a power-law acceleration. The expressions for the transient and the stationary average degree distributions are obtained by using the Poisson process. This result shows that the model generates appropriate power-law connectivity distributions. Therefore, we find a power-law acceleration invariance of the scale-free networks. The numerical simulations of the models agree with the analytical results well.

Effects of Scale-Free Topological Properties on Dynamical Synchronization and Control in Coupled Map Lattices

In the paper, we study effects of scale-free （SF） topology on dynamical synchronization and control in coupled map lattices （CIVIL）. Our strategy is to apply three feedback control methods, including constant feedback and two types of time-delayed feedback, to a small fraction of network nodes to reach desired synchronous state. Two controlled bifurcation diagrams verses feedback strength are obtained respectively. It is found that the value of critical feedback strength γc for the first time-delayed feedback control is increased linearly as e is increased linearly. The GML with SF loses synchronization and intermittency occurs if γ 〉 γc. Numerical examples are presented to demonstrate all results.

A novel scale-free network model based on clique growth

A novel scale-flee network model based on clique （complete subgraph of random size） growth and preferential attachment was proposed. The simulations of this model were carried out. And the necessity of two evolving mechanisms of the model was verified. According to the mean-field theory, the degree distribution of this model was analyzed and computed. The degree distribution function of vertices of the generating network P（d） is 2m^2m1^-3（d-m1 ＋ 1）^-3, where m and m1 denote the number of the new adding edges and the vertex number of the cliques respectively, d is the degree of the vertex, while one of cliques P（k） is 2m^2Ek^-3, where k is the degree of the clique. The simulated and analytical results show that both the degree distributions of vertices and cliques follow the scale-flee power-law distribution. The scale-free property of this model disappears in the absence of any one of the evolving mechanisms. Moreover, the randomicity of this model increases with the increment of the vertex number of the cliques.

Generalized minimum information path routing strategy on scale-free networks

This paper presents a new routing strategy by introducing a tunable parameter into the minimum information path routing strategy we proposed previously. It is found that network transmission capacity can be considerably enhanced by adjusting the parameter with various allocations of node capability for packet delivery. Moreover, the proposed routing strategy provides a traffic load distribution which can better match the allocation of node capability than that of traditional efficient routing strategies, leading to a network with improved transmission performance. This routing strategy, without deviating from the shortest-path routing strategy in the length of paths too much, produces improved performance indexes such as critical generating rate, average length of paths and average search information.

Enhancement of scale-free network attack tolerance

Despite the large size of most communication and transportation systems, there are short paths between nodes in these networks which guarantee the efficient information, data and passenger delivery; furthermore these networks have a surprising tolerance under random errors thanks to their inherent scale-free topology. However, their scale-free topology also makes them fragile under intentional attacks, leaving us a challenge on how to improve the network robustness against intentional attacks without losing their strong tolerance under random errors and high message and passenger delivering capacity. Here We propose two methods （SL method and SH method） to enhance scale-free network＇s tolerance under attack in different conditions.

Scale-free Structure of Town Road Network in Southern Jiangsu Province of China

From the viewpoint of Graph Theory this paper builds a town road network graph of regional scale, and proposes numerical vertex degree （Di）, rank vertex degree （Dr） and population size vertex degree （Dp） on the base of vertex degree （D）. Then the indicators of Di, Dr, Op and mathematical statistics methods are applied to investigating scale-free structure of town road networks in the southern Jiangsu Province. The results show that the distribution of Oi does not exhibit scale-free properties, but Dr and Dp do. Additionally the correlation coefficient between Dp and Di is only 0.569, but the spatial correlation between Dp and Dr is very evident on the base of correlation analysis and spatial analysis of GIS. The mutual mechanism between Dp and Dr spatially represents a ＂Core-Belt＂ model of town development of regional scale. The town development model is open and clustered, and beneficial to both economic development and ecological protection. And then we suggest that Suzhou City, Wuxi City, Changzhou City and Wujin City control towns＇ high-density pattern by conducting centralization and consolidation policies, and properly controlling and planning higher rank roads; whereas Nanjing City, Zhenjiang City, Jintan City and Liyang City must strengthen the development of towns along higher rank roads.