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Convergence speed of consensus problems over undirected scale-free networks
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作者 孙巍 窦丽华 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第12期135-143,共9页
Scale-free networks and consensus behaviour among multiple agents have both attracted much attention. To investigate the consensus speed over scale-free networks is the major topic of the present work. A novel method ... Scale-free networks and consensus behaviour among multiple agents have both attracted much attention. To investigate the consensus speed over scale-free networks is the major topic of the present work. A novel method is developed to construct scale-free networks due to their remarkable power-law degree distributions, while preserving the diversity of network topologies. The time cost or iterations for networks to reach a certain level of consensus is discussed, considering the influence from power-law parameters. They are both demonstrated to be reversed power-law functions of the algebraic connectivity, which is viewed as a measurement on convergence speed of the consensus behaviour. The attempts of tuning power-law parameters may speed up the consensus procedure, but it could also make the network less robust over time delay at the same time. Large scale of simulations are supportive to the conclusions. 展开更多
关键词 scale-free networks CONSENSUS power-law distribution
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Spontaneous Recovery in Directed Dynamical Networks
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作者 Xueming Liu Xian Yan H.Eugene Stanley 《Engineering》 SCIE EI CAS CSCD 2024年第6期208-214,共7页
Complex networked systems,which range from biological systems in the natural world to infrastructure systems in the human-made world,can exhibit spontaneous recovery after a failure;for example,a brain may spontaneous... Complex networked systems,which range from biological systems in the natural world to infrastructure systems in the human-made world,can exhibit spontaneous recovery after a failure;for example,a brain may spontaneously return to normal after a seizure,and traffic flow can become smooth again after a jam.Previous studies on the spontaneous recovery of dynamical networks have been limited to undirected networks.However,most real-world networks are directed.To fill this gap,we build a model in which nodes may alternately fail and recover,and we develop a theoretical tool to analyze the recovery properties of directed dynamical networks.We find that the tool can accurately predict the final fraction of active nodes,and the prediction accuracy decreases as the fraction of bidirectional links in the network increases,which emphasizes the importance of directionality in network dynamics.Due to different initial states,directed dynamical networks may show alternative stable states under the same control parameter,exhibiting hysteresis behavior.In addition,for networks with finite sizes,the fraction of active nodes may jump back and forth between high and low states,mimicking repetitive failure-recovery processes.These findings could help clarify the system recovery mechanism and enable better design of networked systems with high resilience. 展开更多
关键词 network resilience directed dynamical networks Spontaneous recovery
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Estimation of the anisotropy of hydraulic conductivity through 3D fracture networks using the directional geological entropy 被引量:1
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作者 Chuangbing Zhou Zuyang Ye +2 位作者 Chi Yao Xincheng Fan Feng Xiong 《International Journal of Mining Science and Technology》 SCIE EI CAS CSCD 2024年第2期137-148,共12页
With an extension of the geological entropy concept in porous media,the approach called directional entrogram is applied to link hydraulic behavior to the anisotropy of the 3D fracture networks.A metric called directi... With an extension of the geological entropy concept in porous media,the approach called directional entrogram is applied to link hydraulic behavior to the anisotropy of the 3D fracture networks.A metric called directional entropic scale is used to measure the anisotropy of spatial order in different directions.Compared with the traditional connectivity indexes based on the statistics of fracture geometry,the directional entropic scale is capable to quantify the anisotropy of connectivity and hydraulic conductivity in heterogeneous 3D fracture networks.According to the numerical analysis of directional entrogram and fluid flow in a number of the 3D fracture networks,the hydraulic conductivities and entropic scales in different directions both increase with spatial order(i.e.,trace length decreasing and spacing increasing)and are independent of the dip angle.As a result,the nonlinear correlation between the hydraulic conductivities and entropic scales from different directions can be unified as quadratic polynomial function,which can shed light on the anisotropic effect of spatial order and global entropy on the heterogeneous hydraulic behaviors. 展开更多
关键词 3D fracture network Geological entropy directional entropic scale ANISOTROPY Hydraulic conductivity
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Percolation transitions in edge-coupled interdependent networks with directed dependency links
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作者 高彦丽 于海波 +2 位作者 周杰 周银座 陈世明 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第9期586-595,共10页
We propose a model of edge-coupled interdependent networks with directed dependency links(EINDDLs)and develop the theoretical analysis framework of this model based on the self-consistent probabilities method.The phas... We propose a model of edge-coupled interdependent networks with directed dependency links(EINDDLs)and develop the theoretical analysis framework of this model based on the self-consistent probabilities method.The phase transition behaviors and parameter thresholds of this model under random attacks are analyzed theoretically on both random regular(RR)networks and Erd¨os-Renyi(ER)networks,and computer simulations are performed to verify the results.In this EINDDL model,a fractionβof connectivity links within network B depends on network A and a fraction(1-β)of connectivity links within network A depends on network B.It is found that randomly removing a fraction(1-p)of connectivity links in network A at the initial state,network A exhibits different types of phase transitions(first order,second order and hybrid).Network B is rarely affected by cascading failure whenβis small,and network B will gradually converge from the first-order to the second-order phase transition asβincreases.We present the critical values ofβfor the phase change process of networks A and B,and give the critical values of p andβfor network B at the critical point of collapse.Furthermore,a cascading prevention strategy is proposed.The findings are of great significance for understanding the robustness of EINDDLs. 展开更多
关键词 edge-coupled interdependent networks with directed dependency links percolation transitions cascading failures robustness analysis
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Generation of scale-free knowledge network with local world mechanism
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作者 单海燕 王文平 《Journal of Southeast University(English Edition)》 EI CAS 2009年第4期545-548,共4页
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 distribu... 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. 展开更多
关键词 knowledge network network structure scale-free local world mechanism
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Exploring evolutionary features of directed weighted hazard network in the subway construction 被引量:3
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作者 Gong-Yu Hou Cong Jin +2 位作者 Zhe-Dong Xu Ping Yu Yi-Yi Cao 《Chinese Physics B》 SCIE EI CAS CSCD 2019年第3期399-407,共9页
A better understanding of previous accidents is an effective way to reduce the occurrence of similar accidents in the future. In this paper, a complex network approach is adopted to construct a directed weighted hazar... A better understanding of previous accidents is an effective way to reduce the occurrence of similar accidents in the future. In this paper, a complex network approach is adopted to construct a directed weighted hazard network(DWHN) to analyze topological features and evolution of accidents in the subway construction. The nodes are hazards and accidents, the edges are multiple relationships of these nodes and the weight of edges are occurrence times of repetitive relationships. The results indicate that the DWHN possesses the property of small-world with small average path length and large clustering coefficient, indicating that hazards have better connectivity and will spread widely and quickly in the network. Moreover,the DWHN has the property of scale-free network for the cumulative degree distribution follows a power-law distribution.It makes DWHN more vulnerable to target attacks. Controlling key nodes with higher degree, strength and betweenness centrality will destroy the connectivity of DWHN and mitigate the spreading of accidents in the network. This study is helpful for discovering inner relationships and evolutionary features of hazards and accidents in the subway construction. 展开更多
关键词 ACCIDENT analysis directed WEIGHTED network complex network EVOLUTIONARY FEATURES
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Immunization for scale-free networks by random walker 被引量:7
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作者 胡柯 唐翌 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第12期2782-2787,共6页
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 ... 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. 展开更多
关键词 immunization strategy scale-free network random walk intentional random walk
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Circular Formation Flight Control for Unmanned Aerial Vehicles With Directed Network and External Disturbance 被引量:11
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作者 Yangyang Chen Rui Yu +1 位作者 Ya Zhang Chenglin Liu 《IEEE/CAA Journal of Automatica Sinica》 EI CSCD 2020年第2期505-516,共12页
This paper proposes a new distributed formation flight protocol for unmanned aerial vehicles(UAVs)to perform coordinated circular tracking around a set of circles on a target sphere.Different from the previous results... This paper proposes a new distributed formation flight protocol for unmanned aerial vehicles(UAVs)to perform coordinated circular tracking around a set of circles on a target sphere.Different from the previous results limited in bidirectional networks and disturbance-free motions,this paper handles the circular formation flight control problem with both directed network and spatiotemporal disturbance with the knowledge of its upper bound.Distinguishing from the design of a common Lyapunov fiunction for bidirectional cases,we separately design the control for the circular tracking subsystem and the formation keeping subsystem with the circular tracking error as input.Then the whole control system is regarded as a cascade connection of these two subsystems,which is proved to be stable by input-tostate stability(ISS)theory.For the purpose of encountering the external disturbance,the backstepping technology is introduced to design the control inputs of each UAV pointing to North and Down along the special sphere(say,the circular tracking control algorithm)with the help of the switching function.Meanwhile,the distributed linear consensus protocol integrated with anther switching anti-interference item is developed to construct the control input of each UAV pointing to east along the special sphere(say,the formation keeping control law)for formation keeping.The validity of the proposed control law is proved both in the rigorous theory and through numerical simulations. 展开更多
关键词 directed network external disturbance flight control unmanned aerial vehicles(UAVs)
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Improving Dendritic Neuron Model With Dynamic Scale-Free Network-Based Differential Evolution 被引量:3
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作者 Yang Yu Zhenyu Lei +3 位作者 Yirui Wang Tengfei Zhang Chen Peng Shangce Gao 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2022年第1期99-110,共12页
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 we... 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. 展开更多
关键词 Artificial neuron networks(ANNs) dendrite neuron network differential evolution(DE) scale-free network
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Epidemic spreading in scale-free networks including the effect of individual vigilance 被引量:2
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作者 Gong Yong-Wang Song Yu-Rong Jiang Guo-Ping 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第1期41-45,共5页
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 sprea... 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. 展开更多
关键词 scale-free network susceptible-infected-recovered model individual vigilance epidemicthreshold
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Cascading failure in the wireless sensor scale-free networks 被引量:2
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作者 刘浩然 董明如 +1 位作者 尹荣荣 韩丽 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第5期293-299,共7页
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 t... 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. 展开更多
关键词 wireless sensor network scale-free topology cascading failure
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Reliability Evaluation of Two-Stage Directed Semi-Markov Repairable Network Systems 被引量:2
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作者 Ruiqin Fan Liying Wang Tongliang Li 《Applied Mathematics》 2013年第4期690-693,共4页
A two-stage directed Semi-Markov repairable network system is presented in this paper to model the performance of many transmission systems, such as power or oil transmission network, water or gas supply network, etc.... A two-stage directed Semi-Markov repairable network system is presented in this paper to model the performance of many transmission systems, such as power or oil transmission network, water or gas supply network, etc. The availability of the system is discussed by using Markov renewal theory, Laplace transform and probability analysis methods. A numerical example is given to illustrate the results obtained in the paper. 展开更多
关键词 directed network SYSTEM Reliability AVAILABILITY Semi-Markov REPAIRABLE SYSTEM MARKOV RENEWAL Process
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FIXED/PREASSIGNED-TIME SYNCHRONIZATION OF QUATERNION-VALUED NEURAL NETWORKS INVOLVING DELAYS AND DISCONTINUOUS ACTIVATIONS: A DIRECT APPROACH
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作者 魏琬璐 胡成 +1 位作者 于娟 蒋海军 《Acta Mathematica Scientia》 SCIE CSCD 2023年第3期1439-1461,共23页
The fixed-time synchronization and preassigned-time synchronization are investigated for a class of quaternion-valued neural networks with time-varying delays and discontinuous activation functions. Unlike previous ef... The fixed-time synchronization and preassigned-time synchronization are investigated for a class of quaternion-valued neural networks with time-varying delays and discontinuous activation functions. Unlike previous efforts that employed separation analysis and the real-valued control design, based on the quaternion-valued signum function and several related properties, a direct analytical method is proposed here and the quaternion-valued controllers are designed in order to discuss the fixed-time synchronization for the relevant quaternion-valued neural networks. In addition, the preassigned-time synchronization is investigated based on a quaternion-valued control design, where the synchronization time is preassigned and the control gains are finite. Compared with existing results, the direct method without separation developed in this article is beneficial in terms of simplifying theoretical analysis, and the proposed quaternion-valued control schemes are simpler and more effective than the traditional design, which adds four real-valued controllers. Finally, two numerical examples are given in order to support the theoretical results. 展开更多
关键词 fixed-time synchronization preassigned-time synchronization quaternion-valued neural networks discontinuous activation direct analysis method
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Malicious Code Modeling and Analysis in Weighted Scale-Free Networks 被引量:2
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作者 WANG Changguang WANG Fangwei +1 位作者 ZHANG Yangkai MA Jianfengi 《Wuhan University Journal of Natural Sciences》 CAS 2007年第1期51-54,共4页
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... 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. 展开更多
关键词 malicious code weighted scale-free networks propagation model
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Distributed Fault-Tolerant Containment Control for Nonlinear Multi-Agent Systems Under Directed Network Topology via Hierarchical Approach 被引量:3
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作者 Shuyi Xiao Jiuxiang Dong 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2021年第4期806-816,共11页
This paper investigates the distributed fault-tolerant containment control(FTCC)problem of nonlinear multi-agent systems(MASs)under a directed network topology.The proposed control framework which is independent on th... This paper investigates the distributed fault-tolerant containment control(FTCC)problem of nonlinear multi-agent systems(MASs)under a directed network topology.The proposed control framework which is independent on the global information about the communication topology consists of two layers.Different from most existing distributed fault-tolerant control(FTC)protocols where the fault in one agent may propagate over network,the developed control method can eliminate the phenomenon of fault propagation.Based on the hierarchical control strategy,the FTCC problem with a directed graph can be simplified to the distributed containment control of the upper layer and the fault-tolerant tracking control of the lower layer.Finally,simulation results are given to demonstrate the effectiveness of the proposed control protocol. 展开更多
关键词 Adaptive fault-tolerant control directed network topology distributed control hierarchical control multi-agent systems(MASs)
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Epidemic spreading on a scale-free network with awareness 被引量:1
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作者 鲁延玲 蒋国平 宋玉蓉 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第10期44-48,共5页
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 mo... 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. 展开更多
关键词 scale-free network AWARENESS VACCINATION epidemic threshold
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Degree distribution and robustness of cooperative communication network with scale-free model 被引量:1
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作者 王建荣 王建萍 +1 位作者 何振 许海涛 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第6期115-121,共7页
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 atta... 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. 展开更多
关键词 cooperative communication complex networks scale-free degree distribution ROBUSTNESS
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Adaptive local routing strategy on a scale-free network 被引量:1
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作者 刘锋 赵寒 +2 位作者 李明 任丰原 朱衍波 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第4期159-167,共9页
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... 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. 展开更多
关键词 local routing scale-free networks preferential probability traffic load
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Enhancement of scale-free network attack tolerance 被引量:1
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作者 瞿泽辉 王 璞 +1 位作者 宋朝鸣 秦志光 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第11期7-12,共6页
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 ... 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. 展开更多
关键词 scale-free network robustness spatial limited network attack tolerance
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Bee Colony Optimization Algorithm for Routing and Wavelength Assignment Based on Directional Guidance in Satellite Optical Networks
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作者 Mai Yang Qi Zhang +8 位作者 Haipeng Yao Ran Gao Xiangjun Xin Feng Tian Weiying Feng Dong Chen Fu Wang Qinghua Tian Jinxi Qian 《China Communications》 SCIE CSCD 2023年第7期89-107,共19页
With the development of satellite communication,in order to solve the problems of shortage of on-board resources and refinement of delay requirements to improve the communication performance of satellite optical netwo... With the development of satellite communication,in order to solve the problems of shortage of on-board resources and refinement of delay requirements to improve the communication performance of satellite optical networks,this paper proposes a bee colony optimization algorithm for routing and wavelength assignment based on directional guidance(DBCO-RWA)in satellite optical networks.In D-BCORWA,directional guidance based on relative position and link load is defined,and then the link cost function in the path search stage is established based on the directional guidance factor.Finally,feasible solutions are expanded in the global optimization stage.The wavelength utilization,communication success probability,blocking rate,communication hops and convergence characteristic are simulated.The results show that the performance of the proposed algorithm is improved compared with existing algorithms. 展开更多
关键词 routing and wavelength assignment satel-lite optical networks bee colony optimization algo-rithm directional guidance feasible solution extension
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