Complex network models are frequently employed for simulating and studyingdiverse real-world complex systems.Among these models,scale-free networks typically exhibit greater fragility to malicious attacks.Consequently...Complex network models are frequently employed for simulating and studyingdiverse real-world complex systems.Among these models,scale-free networks typically exhibit greater fragility to malicious attacks.Consequently,enhancing the robustness of scale-free networks has become a pressing issue.To address this problem,this paper proposes a Multi-Granularity Integration Algorithm(MGIA),which aims to improve the robustness of scale-free networks while keeping the initial degree of each node unchanged,ensuring network connectivity and avoiding the generation of multiple edges.The algorithm generates a multi-granularity structure from the initial network to be optimized,then uses different optimization strategies to optimize the networks at various granular layers in this structure,and finally realizes the information exchange between different granular layers,thereby further enhancing the optimization effect.We propose new network refresh,crossover,and mutation operators to ensure that the optimized network satisfies the given constraints.Meanwhile,we propose new network similarity and network dissimilarity evaluation metrics to improve the effectiveness of the optimization operators in the algorithm.In the experiments,the MGIA enhances the robustness of the scale-free network by 67.6%.This improvement is approximately 17.2%higher than the optimization effects achieved by eight currently existing complex network robustness optimization algorithms.展开更多
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
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 considerab...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.展开更多
In this paper a new model for the spread of sexually transmitted diseases （STDs） is presented. The dynamic behaviors of the model on a heterogenons scale-free （SF） network are considered, where the absence of a th...In this paper a new model for the spread of sexually transmitted diseases （STDs） is presented. The dynamic behaviors of the model on a heterogenons scale-free （SF） network are considered, where the absence of a threshold on the SF network is demonstrated, and the stability of the disease-free equilibrium is obtained. Three immunization strategies, uniform immunization, proportional immunization and targeted immunization, are applied in this model. Analytical and simulated results are given to show that the proportional immunization strategy in the model is effective on SF networks.展开更多
A novel immunization strategy called the random walk immunization strategy on scale-free networks is proposed. Different from other known immunization strategies, this strategy works as follows： a node is randomly ch...A novel immunization strategy called the random walk immunization strategy on scale-free networks is proposed. Different from other known immunization strategies, this strategy works as follows： a node is randomly chosen from the network. Starting from this node, randomly walk to one of its neighbor node; if the present node is not immunized, then immunize it and continue the random walk; otherwise go back to the previous node and randomly walk again. This process is repeated until a certain fraction of nodes is immunized. By theoretical analysis and numerical simulations, we found that this strategy is very effective in comparison with the other known immunization strategies.展开更多
Most of the realistic networks are weighted scale-free networks. How this structure influences the condensation on it is a challenging problem. Recently, we make a first step to discuss its condensation [Phys. Rev. E ...Most of the realistic networks are weighted scale-free networks. How this structure influences the condensation on it is a challenging problem. Recently, we make a first step to discuss its condensation [Phys. Rev. E 74 （2006） 036101] and here we focus on its evolutionary process of phase transition. In order to show how the weighted transport influences the dynamical properties, we study the relaxation dynamics in a zero range process on weighted scale-free networks. We find that there is a hierarchical relaxation dynamics in the evolution and there is a scaling relation between the relaxation time and the jumping exponent. The relaxation dynamics can be illustrated by a mean-field equation. The theoretical predictions are confirmed by our numerical simulations.展开更多
A simple model for a set of interacting idealized neurons in scale-free networks is introduced. The basic elements of the model are endowed with the main features of a neuron function. We find that our model displays ...A simple model for a set of interacting idealized neurons in scale-free networks is introduced. The basic elements of the model are endowed with the main features of a neuron function. We find that our model displays powerlaw behavior of avalanche sizes and generates long-range temporal correlation. More importantly, we find different dynamical behavior for nodes with different connectivity in the scale-free networks.展开更多
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
A modified Olami-Feder-Christenaen model of self-organized criticality on generalized Barabási-Albert （GBA） scale-flee networks is investigated. We find that our mode/ displays power-law behavior and the avalan...A modified Olami-Feder-Christenaen model of self-organized criticality on generalized Barabási-Albert （GBA） scale-flee networks is investigated. We find that our mode/ displays power-law behavior and the avalanche dynamical behavior is sensitive to the topological structure of networks. Furthermore, the exponent ~ of the model depends on b, which weights the distance in comparison with the degree in the GBA network evolution.展开更多
A modified evolution model of self-organized criticality on generalized Barabasi-Albert （GBA）.scale-free networks is investigated. In our model, we find that spatial and temporal correlations exhibit critical behavi...A modified evolution model of self-organized criticality on generalized Barabasi-Albert （GBA）.scale-free networks is investigated. In our model, we find that spatial and temporal correlations exhibit critical behaviors. More importantly, these critical behaviors change with the parameter b, which weights the distance in comparison with the degree in the GBA network evolution.展开更多
This paper studies consensus problems in weighted scale-free networks of asymmetrically coupled dynamical units, where the asymmetry in a given link is deter：mined by the relative degree of the involved nodes. It sho...This paper studies consensus problems in weighted scale-free networks of asymmetrically coupled dynamical units, where the asymmetry in a given link is deter：mined by the relative degree of the involved nodes. It shows that the asymmetry of interactions has a great effect on the consensus. Especially, when the interactions are dominant from higher- to lower-degree nodes, both the convergence speed and the robustness to communication delay are enhanced.展开更多
Based on the scale-free network, an integrated systemic inflammatory response syndrome model with artificial immunity, a feedback mechanism, crowd density and the moving activities of an individual can be built. The e...Based on the scale-free network, an integrated systemic inflammatory response syndrome model with artificial immunity, a feedback mechanism, crowd density and the moving activities of an individual can be built. The effects of these factors on the spreading process are investigated through the model. The research results show that the artificial immunity can reduce the stable infection ratio and enhance the spreading threshold of the system. The feedback mechanism can only reduce the stable infection ratio of system, but cannot affect the spreading threshold of the system. The bigger the crowd density is, the higher the infection ratio of the system is and the smaller the spreading threshold is. In addition, the simulations show that the individual movement can enhance the stable infection ratio of the system only under the condition that the spreading rate is high, however, individual movement will reduce the stable infection ratio of the system.展开更多
The dynamics of zero-range processes on complex networks is expected to be influenced by the topological structure of underlying networks.A real space complete condensation phase transition in the stationary state may...The dynamics of zero-range processes on complex networks is expected to be influenced by the topological structure of underlying networks.A real space complete condensation phase transition in the stationary state may occur.We study the finite density effects of the condensation transition in both the stationary and dynamical zero-range processes on scale-free networks.By means of grand canonical ensemble method,we predict analytically the scaling laws of the average occupation number with respect to the finite density for the steady state.We further explore the relaxation dynamics of the condensation phase transition.By applying the hierarchical evolution and scaling ansatz,a scaling law for the relaxation dynamics is predicted.Monte Carlo simulations are performed and the predicted density scaling laws are nicely validated.展开更多
The influence of a node in a network can be characterized by its macroscopic properties such as eigenvector centrality. An issue of significant theoretical and practical interest is to modify the influence or roles of...The influence of a node in a network can be characterized by its macroscopic properties such as eigenvector centrality. An issue of significant theoretical and practical interest is to modify the influence or roles of the nodes in a network, and recent advances indicate that this can be achieved by just controlling a subset of nodes： the socalled controllers. However, the relationship between the structural properties of a network and its controllability, e.g., the control of node importance, is still not well understood. Here we systematically＂ explore this relationship by constructing scale-free networks with a fixed degree sequence and tunable network characteristics. We calculate the relative size （nc＊） of the minimai controlling set required to controi the importance of each individual node in a network. It is found that while clustering has no significant impact on nc＊, changes in degree-degree correlations, heterogeneity and the average degree of networks demonstrate a discernible impact on its controllability.展开更多
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
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
We consider the effect of clustering coefficient on the synchronizability of coupled oscillators located on scale-free networks. The analytic result for the value of clustering coefficient aiming at a highly clustered...We consider the effect of clustering coefficient on the synchronizability of coupled oscillators located on scale-free networks. The analytic result for the value of clustering coefficient aiming at a highly clustered scale-free network model, the Holme-Kim model is obtained, and the relationship between network synchronizability and clustering coefficient is reported. The simulation results strongly suggest that the more clustered the network, the poorer the synchronizability.展开更多
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
A continuum opinion dynamic model is presented based on two rules. The first one considers the mobilities of the individuals, the second one supposes that the individuals update their opinions independently. The resul...A continuum opinion dynamic model is presented based on two rules. The first one considers the mobilities of the individuals, the second one supposes that the individuals update their opinions independently. The results of the model indicate that the bounded confidence εc, separating consensus and incoherent states, of a scale-free network is much smaller than the one of a lattice. If the system can reach the consensus state, the sum of all individuals＇ opinion change Oc（t） quickly decreases in an exponential form, while if it reaches the incoherent state finally, Oc（t） decreases slowly and has the punctuated equilibrium characteristic.展开更多
As a classical complex network model, scale-free network is widely used and studied. And motifs, as a high-order subgraph structure, frequently appear in scale-free networks, and have a great influence on the structur...As a classical complex network model, scale-free network is widely used and studied. And motifs, as a high-order subgraph structure, frequently appear in scale-free networks, and have a great influence on the structural integrity, functional integrity and dynamics of the networks. In order to overcome the shortcomings in the existing work on the robustness of complex networks, only nodes or edges are considered, while the defects of high-order structure in the network are ignored.From the perspective of network motif, we propose an entropy of node degree distribution based on motif to measure the robustness of scale-free networks under random attacks. The effectiveness and superiority of our method are verified and analyzed in the BA scale-free networks.展开更多
基金National Natural Science Foundation of China(11971211,12171388).
文摘Complex network models are frequently employed for simulating and studyingdiverse real-world complex systems.Among these models,scale-free networks typically exhibit greater fragility to malicious attacks.Consequently,enhancing the robustness of scale-free networks has become a pressing issue.To address this problem,this paper proposes a Multi-Granularity Integration Algorithm(MGIA),which aims to improve the robustness of scale-free networks while keeping the initial degree of each node unchanged,ensuring network connectivity and avoiding the generation of multiple edges.The algorithm generates a multi-granularity structure from the initial network to be optimized,then uses different optimization strategies to optimize the networks at various granular layers in this structure,and finally realizes the information exchange between different granular layers,thereby further enhancing the optimization effect.We propose new network refresh,crossover,and mutation operators to ensure that the optimized network satisfies the given constraints.Meanwhile,we propose new network similarity and network dissimilarity evaluation metrics to improve the effectiveness of the optimization operators in the algorithm.In the experiments,the MGIA enhances the robustness of the scale-free network by 67.6%.This improvement is approximately 17.2%higher than the optimization effects achieved by eight currently existing complex network robustness optimization algorithms.
基金Supported by the National Natural Science Foundation of China (90204012, 60573036) and the Natural Science Foundation of Hebei Province (F2006000177)
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60972165)the National High Technology Project of China (Grant No. 2007AA11Z210)+2 种基金the Doctoral Fund of Ministry of Education of China (Grant Nos. 20100092120012,20070286004)the Foundation of High Technology Project in Jiangsu Province,the Natural Science Foundation of Jiangsu Province(Grant No. BK2010240)the Special Scientific Foundation for the"Eleventh-Five-Year" Plan of China
文摘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.
文摘In this paper a new model for the spread of sexually transmitted diseases （STDs） is presented. The dynamic behaviors of the model on a heterogenons scale-free （SF） network are considered, where the absence of a threshold on the SF network is demonstrated, and the stability of the disease-free equilibrium is obtained. Three immunization strategies, uniform immunization, proportional immunization and targeted immunization, are applied in this model. Analytical and simulated results are given to show that the proportional immunization strategy in the model is effective on SF networks.
基金supported by the National Natural Science Foundation of China (No.60774088)the Program for New Century Excellent Talents in University of China (No.NCET-2005-229)the Science and Technology Research Key Project of Education Ministry of China (No.107024)
文摘A novel immunization strategy called the random walk immunization strategy on scale-free networks is proposed. Different from other known immunization strategies, this strategy works as follows： a node is randomly chosen from the network. Starting from this node, randomly walk to one of its neighbor node; if the present node is not immunized, then immunize it and continue the random walk; otherwise go back to the previous node and randomly walk again. This process is repeated until a certain fraction of nodes is immunized. By theoretical analysis and numerical simulations, we found that this strategy is very effective in comparison with the other known immunization strategies.
基金The project supported by National Natural Science Foundation of China under Grant Nos.10475027 and 10635040the Pujiang Project of Shanghai under Grant No.05PJ14036+1 种基金the Shuguang Project of Shanghai under Grant No.05SG27the New Century Excellent Talent Project of the Ministry of Education of China under Grant No.-05-0424
文摘Most of the realistic networks are weighted scale-free networks. How this structure influences the condensation on it is a challenging problem. Recently, we make a first step to discuss its condensation [Phys. Rev. E 74 （2006） 036101] and here we focus on its evolutionary process of phase transition. In order to show how the weighted transport influences the dynamical properties, we study the relaxation dynamics in a zero range process on weighted scale-free networks. We find that there is a hierarchical relaxation dynamics in the evolution and there is a scaling relation between the relaxation time and the jumping exponent. The relaxation dynamics can be illustrated by a mean-field equation. The theoretical predictions are confirmed by our numerical simulations.
基金The project supported by National Natural Science Foundation of China under Grant No. 90203008 and the Doctoral Foundation of the Ministry of Education of China.
文摘A simple model for a set of interacting idealized neurons in scale-free networks is introduced. The basic elements of the model are endowed with the main features of a neuron function. We find that our model displays powerlaw behavior of avalanche sizes and generates long-range temporal correlation. More importantly, we find different dynamical behavior for nodes with different connectivity in the scale-free networks.
基金Project supported by the National Natural Science Foundation for Distinguished Young Scholars of China (Grant No. 60925011)
文摘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.
基金The project supported by National Natural Science Foundation of China under Grant No. 90203008 and the Doctoral Foundation of the Ministry of Education of China
文摘A modified Olami-Feder-Christenaen model of self-organized criticality on generalized Barabási-Albert （GBA） scale-flee networks is investigated. We find that our mode/ displays power-law behavior and the avalanche dynamical behavior is sensitive to the topological structure of networks. Furthermore, the exponent ~ of the model depends on b, which weights the distance in comparison with the degree in the GBA network evolution.
基金The project supported by National Natural Science Foundation of China under Grant No. 90203008 and the Doctoral Foundation of Ministry of Education of China
文摘A modified evolution model of self-organized criticality on generalized Barabasi-Albert （GBA）.scale-free networks is investigated. In our model, we find that spatial and temporal correlations exhibit critical behaviors. More importantly, these critical behaviors change with the parameter b, which weights the distance in comparison with the degree in the GBA network evolution.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10775060 and 10805033)the Doctoral Education Foundation of National Education Committeethe Natural Science Foundation of Gansu Province
文摘This paper studies consensus problems in weighted scale-free networks of asymmetrically coupled dynamical units, where the asymmetry in a given link is deter：mined by the relative degree of the involved nodes. It shows that the asymmetry of interactions has a great effect on the consensus. Especially, when the interactions are dominant from higher- to lower-degree nodes, both the convergence speed and the robustness to communication delay are enhanced.
基金Project supported by the Natural Science Foundation of the Education Department of Guizhou Province,China (Grant No.20090133)International Cooperative Foundation of Guizhou Province,China (Grant No.20117007)
文摘Based on the scale-free network, an integrated systemic inflammatory response syndrome model with artificial immunity, a feedback mechanism, crowd density and the moving activities of an individual can be built. The effects of these factors on the spreading process are investigated through the model. The research results show that the artificial immunity can reduce the stable infection ratio and enhance the spreading threshold of the system. The feedback mechanism can only reduce the stable infection ratio of system, but cannot affect the spreading threshold of the system. The bigger the crowd density is, the higher the infection ratio of the system is and the smaller the spreading threshold is. In addition, the simulations show that the individual movement can enhance the stable infection ratio of the system only under the condition that the spreading rate is high, however, individual movement will reduce the stable infection ratio of the system.
基金the National Natural Science Foundation of China(Grant No.11505115).
文摘The dynamics of zero-range processes on complex networks is expected to be influenced by the topological structure of underlying networks.A real space complete condensation phase transition in the stationary state may occur.We study the finite density effects of the condensation transition in both the stationary and dynamical zero-range processes on scale-free networks.By means of grand canonical ensemble method,we predict analytically the scaling laws of the average occupation number with respect to the finite density for the steady state.We further explore the relaxation dynamics of the condensation phase transition.By applying the hierarchical evolution and scaling ansatz,a scaling law for the relaxation dynamics is predicted.Monte Carlo simulations are performed and the predicted density scaling laws are nicely validated.
基金Supported by Foundations of SiChuan Educational Committee under Grant No 13ZB0198the National Natural Science Foundation of China under Grant Nos 61104224,81373531,61104143 and 61573107The Science and Technology Fund Project of SWPU(2013XJR011)
文摘The influence of a node in a network can be characterized by its macroscopic properties such as eigenvector centrality. An issue of significant theoretical and practical interest is to modify the influence or roles of the nodes in a network, and recent advances indicate that this can be achieved by just controlling a subset of nodes： the socalled controllers. However, the relationship between the structural properties of a network and its controllability, e.g., the control of node importance, is still not well understood. Here we systematically＂ explore this relationship by constructing scale-free networks with a fixed degree sequence and tunable network characteristics. We calculate the relative size （nc＊） of the minimai controlling set required to controi the importance of each individual node in a network. It is found that while clustering has no significant impact on nc＊, changes in degree-degree correlations, heterogeneity and the average degree of networks demonstrate a discernible impact on its controllability.
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant No.60874091)the Six Projects Sponsoring Talent Summits of Jiangsu Province,China(Grant No.SJ209006)+1 种基金the Natural Science Foundation of Jiangsu Province,China(Grant No.BK2010526)the Graduate Student Innovation Research Project of Jiangsu Province,China(Grant No.CXLX110417)
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10532060, 10547004, 10472116, 70571074, 70471033 and 70271070, and the Specialized Programme of the President Fund of Chinese Academy of Science （2006-2007）.
文摘We consider the effect of clustering coefficient on the synchronizability of coupled oscillators located on scale-free networks. The analytic result for the value of clustering coefficient aiming at a highly clustered scale-free network model, the Holme-Kim model is obtained, and the relationship between network synchronizability and clustering coefficient is reported. The simulation results strongly suggest that the more clustered the network, the poorer the synchronizability.
基金supported by the Natural Science Foundation of Hebei Province,China(Grant No.F2014203239)the Autonomous Research Fund of Young Teacher in Yanshan University(Grant No.14LGB017)Yanshan University Doctoral Foundation,China(Grant No.B867)
文摘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.
基金Supported by the National Basic Research Programme of China under Grant No 2006CB705500, the National Natural Science Foundation of China under Grant Nos 10635040, 10532060, 70571074 and 10472116, the Special Research Funds for Theoretical Physics Frontier Problems （A0524701）, the President Fund of Chinese Academy of Sciences, the Specialized Research Fund for the Doctoral Programme of Higher Education of China, and the Research Fund of the Education Department of Liaoning Province （20060140）. The authors thank Dr Ming Zhao for her comments and suggestions.
文摘A continuum opinion dynamic model is presented based on two rules. The first one considers the mobilities of the individuals, the second one supposes that the individuals update their opinions independently. The results of the model indicate that the bounded confidence εc, separating consensus and incoherent states, of a scale-free network is much smaller than the one of a lattice. If the system can reach the consensus state, the sum of all individuals＇ opinion change Oc（t） quickly decreases in an exponential form, while if it reaches the incoherent state finally, Oc（t） decreases slowly and has the punctuated equilibrium characteristic.
基金Project supported by the National Natural Science Foundation of China (Grant No. 62006169)the Youth Natural Science Foundation of Shanxi Province, China (Grant No. 201901D211304)+1 种基金the China Postdoctoral Science Foundation (Grant No. 2021M692400)the Science and Technology Innovation Projects of Universities in Shanxi Province, China (Grant No. 2020L0021)。
文摘As a classical complex network model, scale-free network is widely used and studied. And motifs, as a high-order subgraph structure, frequently appear in scale-free networks, and have a great influence on the structural integrity, functional integrity and dynamics of the networks. In order to overcome the shortcomings in the existing work on the robustness of complex networks, only nodes or edges are considered, while the defects of high-order structure in the network are ignored.From the perspective of network motif, we propose an entropy of node degree distribution based on motif to measure the robustness of scale-free networks under random attacks. The effectiveness and superiority of our method are verified and analyzed in the BA scale-free networks.
