We investigate how dynamical behaviours of complex motor networks depend on the Newman-Watts small-world (NWSW) connections. Network elements are described by the permanent magnet synchronous motor (PMSM) with the...We investigate how dynamical behaviours of complex motor networks depend on the Newman-Watts small-world (NWSW) connections. Network elements are described by the permanent magnet synchronous motor (PMSM) with the values of parameters at which each individual PMSM is stable. It is found that with the increase of connection probability p, the motor in networks becomes periodic and falls into chaotic motion as p further increases. These phenomena imply that NWSW connections can induce and enhance chaos in motor networks. The possible mechanism behind the action of NWSW connections is addressed based on stability theory.展开更多
Living objects have complex internal and external interactions. The complexity is regulated and controlled by homeostasis, which is the balance of multiple opposing influences. The environmental effects finally guide ...Living objects have complex internal and external interactions. The complexity is regulated and controlled by homeostasis, which is the balance of multiple opposing influences. The environmental effects finally guide the self-organized structure. The living systems are open, dynamic structures performing random, stationary, stochastic, self-organizing processes. The self-organizing procedure is defined by the spatial-temporal fractal structure, which is self-similar both in space and time. The system’s complexity appears in its energetics, which tries the most efficient use of the available energies;for that, it organizes various well-connected networks. The controller of environmental relations is the Darwinian selection on a long-time scale. The energetics optimize the healthy processes tuned to the highest efficacy and minimal loss (minimalization of the entropy production). The organism is built up by morphogenetic rules and develops various networks from the genetic level to the organism. The networks have intensive crosstalk and form a balance in the Nash equilibrium, which is the homeostatic state in healthy conditions. Homeostasis may be described as a Nash equilibrium, which ensures energy distribution in a “democratic” way regarding the functions of the parts in the complete system. Cancer radically changes the network system in the organism. Cancer is a network disease. Deviation from healthy networking appears at every level, from genetic (molecular) to cells, tissues, organs, and organisms. The strong proliferation of malignant tissue is the origin of most of the life-threatening processes. The weak side of cancer development is the change of complex information networking in the system, being vulnerable to immune attacks. Cancer cells are masters of adaptation and evade immune surveillance. This hiding process can be broken by electromagnetic nonionizing radiation, for which the malignant structure has no adaptation strategy. Our objective is to review the different sides of living complexity and use the knowledge to fight against cancer.展开更多
Through empirical analysis of the global structure of the Worldwide Marine Transportation Network (WMTN), we find that the WMTN, a small-world network, exhibits an exponential-like degree distribution. We hereby inv...Through empirical analysis of the global structure of the Worldwide Marine Transportation Network (WMTN), we find that the WMTN, a small-world network, exhibits an exponential-like degree distribution. We hereby investigate the efficiency of the WMTN by employing a simple definition. Compared with many other transportation networks, the WMTN possesses relatively low efficiency. Furthermore, by exploring the relationship between the topological structure and the container throughput, we find that strong correlations exist among the container throughout the degree and the clustering coefficient. Also, considering the navigational process that a ship travels in a real shipping line, we obtain that the weight of a seaport is proportional to the total probability contributed by all the passing shipping lines.展开更多
In some real complex networks, only a few nodes can obtain the global information about the entire networks, but most of the nodes own only local connections therefore own only local information of the networks. A new...In some real complex networks, only a few nodes can obtain the global information about the entire networks, but most of the nodes own only local connections therefore own only local information of the networks. A new local-world evolving network model is proposed in this paper. In the model, not all the nodes obtain local network information, which is different from the local world network model proposed by Li and Chen (LC model). In the LC model, each node has only the local connections therefore owns only local information about the entire networks. Theoretical analysis and numerical simulation show that adjusting the ratio of the number of nodes obtaining the global information of the network to the total number of nodes can effectively control the valuing range for the power-law exponent of the new network. Therefore, if the topological structure of a complex network, especially its exponent of power-law degree distribution, needs controlling, we just add or take away a few nodes which own the global information of the network.展开更多
US flight network,composed of 285airports(nodes)and 3 971flights(edges)is studied.A static network model and a dynamic network model of US flight network are established.Firstly,the characteristics of static network a...US flight network,composed of 285airports(nodes)and 3 971flights(edges)is studied.A static network model and a dynamic network model of US flight network are established.Firstly,the characteristics of static network are analyzed.One finds that such a network is a″small-world″and″scale-free″network.The cumulative degree distributions of weighted network and unweighted network follow″Double Pareto Law″.And the degree exponent of weighted network is smaller than unweighted network.The average shortest-path length is 2.368 9,which is smaller than previous results.The clustering coefficient of unweighted network is 0.637 1and of weighted network is 0.653 6,which are both bigger than previous results.The correlation of degree,unweighted clustering coefficient and weighted clustering coefficient are also discussed.Secondly,the characteristics of dynamic network are studied.The structure of flight network is changing as the time goes by on a day.In rush hours,the network′s character of″scale-free″is stronger than other times.And then the relationships of topological structures and congestion effects are addressed.展开更多
The Small world model has been successfully used to explore the abnormal pattern of brain information processing in some neuropsychiatric diseases, but not engaged in the study of cognitive functions. We apply the sma...The Small world model has been successfully used to explore the abnormal pattern of brain information processing in some neuropsychiatric diseases, but not engaged in the study of cognitive functions. We apply the small-world measures: the clustering coefficient and average path length, to evaluate multi-channel event-related potential activity during the generation of global and local imagery. Results show that the brain functional networks of the global and local imagery generation are both small-world ones. In addition, the local imagery generation has a larger clustering coefficient, while the global imagery generation has a shorter average path length. These results support the global precedence in the global-local imagery generation, and reflect the different processing modes in which global imagery emphasizes particularly on global integration, while local imagery on local specialization. Our results indicate that small-world measures could be applied to quantify the difference of brain activities in different cognitive tasks, and further provide some explanations for cognitive behavior.展开更多
In this paper, we propose a simple model that can generate small-world network with community structure. The network is introduced as a tunable community organization with parameter r, which is directly measured by th...In this paper, we propose a simple model that can generate small-world network with community structure. The network is introduced as a tunable community organization with parameter r, which is directly measured by the ratio of inter- to intra-community connectivity, and a smaller r corresponds to a stronger community structure. The structure properties, including the degree distribution, clustering, the communication efficiency and modularity are also analysed for the network. In addition, by using the Kuramoto model, we investigated the phase synchronization on this network, and found that increasing the fuzziness of community structure will markedly enhance the network synchronizability; however, in an abnormal region (r ≤ 0.001), the network has even worse synchronizability than the case of isolated communities (r = 0). Furthermore, this network exhibits a remarkable synchronization behaviour in topological scales: the oscillators of high densely interconnected communities synchronize more easily, and more rapidly than the whole network.展开更多
When complex networks describe a wide range of systems in nature and society,it is increasingly recognized that the topology of real networks are governed by robust organizing principles.Here we discuss the structural...When complex networks describe a wide range of systems in nature and society,it is increasingly recognized that the topology of real networks are governed by robust organizing principles.Here we discuss the structural metrics such as average path length,clustering coefficient and degree distribution,the main models covering random graphs,small-world and scale-free networks,the interplay between structural properties and the synchronization of complex networks.展开更多
Multiple complex networks, each with different properties and mutually fused, have the problems that the evolving process is time varying and non-equilibrium, network structures are layered and interlacing, and evolvi...Multiple complex networks, each with different properties and mutually fused, have the problems that the evolving process is time varying and non-equilibrium, network structures are layered and interlacing, and evolving characteristics are difficult to be measured. On that account, a dynamic evolving model of complex network with fusion nodes and overlap edges(CNFNOEs) is proposed. Firstly, we define some related concepts of CNFNOEs, and analyze the conversion process of fusion relationship and hierarchy relationship. According to the property difference of various nodes and edges, fusion nodes and overlap edges are subsequently split, and then the CNFNOEs is transformed to interlacing layered complex networks(ILCN). Secondly,the node degree saturation and attraction factors are defined. On that basis, the evolution algorithm and the local world evolution model for ILCN are put forward. Moreover, four typical situations of nodes evolution are discussed, and the degree distribution law during evolution is analyzed by means of the mean field method.Numerical simulation results show that nodes unreached degree saturation follow the exponential distribution with an error of no more than 6%; nodes reached degree saturation follow the distribution of their connection capacities with an error of no more than 3%; network weaving coefficients have a positive correlation with the highest probability of new node and initial number of connected edges. The results have verified the feasibility and effectiveness of the model, which provides a new idea and method for exploring CNFNOE's evolving process and law. Also, the model has good application prospects in structure and dynamics research of transportation network, communication network, social contact network,etc.展开更多
We study the evolutionary snowdrift game in a heterogeneous Newman-Watts small-world network. The heterogeneity of the network is controlled by the number of hubs. It is found that the moderate heterogeneity of the ne...We study the evolutionary snowdrift game in a heterogeneous Newman-Watts small-world network. The heterogeneity of the network is controlled by the number of hubs. It is found that the moderate heterogeneity of the network can promote the cooperation best. Besides, we study how the hubs affect the evolution of cooperative behaviours of the heterogeneous Newman-Watts small-world network. Simulation results show that both the initial states of hubs and the connections between hubs can play an important role. Our work gives a further insight into the effect of hubs on the heterogeneous networks.展开更多
We study the congestion phenomenon in a mathematical model of the data packets traffic in transmission networks as a function of the topology and of the load of the network. Two types of traffic are considered: homoge...We study the congestion phenomenon in a mathematical model of the data packets traffic in transmission networks as a function of the topology and of the load of the network. Two types of traffic are considered: homogeneous and heterogeneous traffic. The congestion phenomenon is studied in stationary conditions through the behaviour of two quantities: the mean travel time of a packet and the mean number of packets that have not reached their destination and are traveling in the network. We define a transformation that maps a network having the small world property (Inet 3037 in our numerical experiments) into a (modified) lattice network that has the same number of nodes. This map changes the capacity of the branches of the graphs representing the networks and can be regarded as an “interpolation” between the two classes of networks. Using this transformation we compare the behaviour of Inet 3037 to the behaviour of a modified rectangular lattice and we study the behaviour of the interpolating networks. This study suggests how to change the network topology and the branch capacities in order to alleviate the congestion phenomenon. In the website: http://www.ceri.uniroma1.it/ceri/zirilli/w6 some auxiliary material including animations and stereo?graphic scenes that helps the understanding of this paper is shown.展开更多
基金Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 50937001)the National Natural Science Foundation of China (Grant Nos. 10862001 and 10947011)the Construction of Key Laboratories in Universities of Guangxi,China (Grant No. 200912)
文摘We investigate how dynamical behaviours of complex motor networks depend on the Newman-Watts small-world (NWSW) connections. Network elements are described by the permanent magnet synchronous motor (PMSM) with the values of parameters at which each individual PMSM is stable. It is found that with the increase of connection probability p, the motor in networks becomes periodic and falls into chaotic motion as p further increases. These phenomena imply that NWSW connections can induce and enhance chaos in motor networks. The possible mechanism behind the action of NWSW connections is addressed based on stability theory.
文摘Living objects have complex internal and external interactions. The complexity is regulated and controlled by homeostasis, which is the balance of multiple opposing influences. The environmental effects finally guide the self-organized structure. The living systems are open, dynamic structures performing random, stationary, stochastic, self-organizing processes. The self-organizing procedure is defined by the spatial-temporal fractal structure, which is self-similar both in space and time. The system’s complexity appears in its energetics, which tries the most efficient use of the available energies;for that, it organizes various well-connected networks. The controller of environmental relations is the Darwinian selection on a long-time scale. The energetics optimize the healthy processes tuned to the highest efficacy and minimal loss (minimalization of the entropy production). The organism is built up by morphogenetic rules and develops various networks from the genetic level to the organism. The networks have intensive crosstalk and form a balance in the Nash equilibrium, which is the homeostatic state in healthy conditions. Homeostasis may be described as a Nash equilibrium, which ensures energy distribution in a “democratic” way regarding the functions of the parts in the complete system. Cancer radically changes the network system in the organism. Cancer is a network disease. Deviation from healthy networking appears at every level, from genetic (molecular) to cells, tissues, organs, and organisms. The strong proliferation of malignant tissue is the origin of most of the life-threatening processes. The weak side of cancer development is the change of complex information networking in the system, being vulnerable to immune attacks. Cancer cells are masters of adaptation and evade immune surveillance. This hiding process can be broken by electromagnetic nonionizing radiation, for which the malignant structure has no adaptation strategy. Our objective is to review the different sides of living complexity and use the knowledge to fight against cancer.
基金Supported by the National Natural Science Foundation of China under Grant Nos 70571027, 10647125, 10635020 and 70401020, and the Program of Introducing Talents of Discipline to Universities under Grant No B08033.
文摘Through empirical analysis of the global structure of the Worldwide Marine Transportation Network (WMTN), we find that the WMTN, a small-world network, exhibits an exponential-like degree distribution. We hereby investigate the efficiency of the WMTN by employing a simple definition. Compared with many other transportation networks, the WMTN possesses relatively low efficiency. Furthermore, by exploring the relationship between the topological structure and the container throughput, we find that strong correlations exist among the container throughout the degree and the clustering coefficient. Also, considering the navigational process that a ship travels in a real shipping line, we obtain that the weight of a seaport is proportional to the total probability contributed by all the passing shipping lines.
基金supported by the Scientific Research Starting Foundation of Hangzhou Dianzi University (Grant No KYS091507073)partly by the National High Technology Research and Development Program of China (Grant No 2005AA147030)
文摘In some real complex networks, only a few nodes can obtain the global information about the entire networks, but most of the nodes own only local connections therefore own only local information of the networks. A new local-world evolving network model is proposed in this paper. In the model, not all the nodes obtain local network information, which is different from the local world network model proposed by Li and Chen (LC model). In the LC model, each node has only the local connections therefore owns only local information about the entire networks. Theoretical analysis and numerical simulation show that adjusting the ratio of the number of nodes obtaining the global information of the network to the total number of nodes can effectively control the valuing range for the power-law exponent of the new network. Therefore, if the topological structure of a complex network, especially its exponent of power-law degree distribution, needs controlling, we just add or take away a few nodes which own the global information of the network.
基金supported by the Projects in the National Science & Technology Pillar Program (2011BAH24B10)the Joint Funds of National Natural Science Foundation of China (61571441)+2 种基金the Fundamental Research Funds for the Central Universities of Civil Aviation University of China in 2016the Open Fund of Air Traffic Management Research Base(No.KGJD201503)the Scientific Research Foundation of Civil Aviation University of China(No.2014QD01S)
文摘US flight network,composed of 285airports(nodes)and 3 971flights(edges)is studied.A static network model and a dynamic network model of US flight network are established.Firstly,the characteristics of static network are analyzed.One finds that such a network is a″small-world″and″scale-free″network.The cumulative degree distributions of weighted network and unweighted network follow″Double Pareto Law″.And the degree exponent of weighted network is smaller than unweighted network.The average shortest-path length is 2.368 9,which is smaller than previous results.The clustering coefficient of unweighted network is 0.637 1and of weighted network is 0.653 6,which are both bigger than previous results.The correlation of degree,unweighted clustering coefficient and weighted clustering coefficient are also discussed.Secondly,the characteristics of dynamic network are studied.The structure of flight network is changing as the time goes by on a day.In rush hours,the network′s character of″scale-free″is stronger than other times.And then the relationships of topological structures and congestion effects are addressed.
基金Supported by the National Natural Science Foundation of China 60971096, and the New Century Excellent Talent Project (NCET) of the Ministry of Education of China under Grant No 06-0277.
文摘The Small world model has been successfully used to explore the abnormal pattern of brain information processing in some neuropsychiatric diseases, but not engaged in the study of cognitive functions. We apply the small-world measures: the clustering coefficient and average path length, to evaluate multi-channel event-related potential activity during the generation of global and local imagery. Results show that the brain functional networks of the global and local imagery generation are both small-world ones. In addition, the local imagery generation has a larger clustering coefficient, while the global imagery generation has a shorter average path length. These results support the global precedence in the global-local imagery generation, and reflect the different processing modes in which global imagery emphasizes particularly on global integration, while local imagery on local specialization. Our results indicate that small-world measures could be applied to quantify the difference of brain activities in different cognitive tasks, and further provide some explanations for cognitive behavior.
基金supported in part by the National Natural Science Foundation of China (Grant Nos. 60673097, 60601029, 60672126and 60702062)the National High-Tech Research and Development Plan of China (Grant Nos. 2009AA12Z210, 2008AA01Z125,2007AA12Z136 and 2007AA12Z223)+1 种基金the National Research Foundation for the Doctoral Program of Higher Education of China (Grant Nos. 20060701007 and 20070701016)Ministry&Commission-Level Research Foundation of China (Grant Nos. XADZ2008159 and 51307040103)
文摘In this paper, we propose a simple model that can generate small-world network with community structure. The network is introduced as a tunable community organization with parameter r, which is directly measured by the ratio of inter- to intra-community connectivity, and a smaller r corresponds to a stronger community structure. The structure properties, including the degree distribution, clustering, the communication efficiency and modularity are also analysed for the network. In addition, by using the Kuramoto model, we investigated the phase synchronization on this network, and found that increasing the fuzziness of community structure will markedly enhance the network synchronizability; however, in an abnormal region (r ≤ 0.001), the network has even worse synchronizability than the case of isolated communities (r = 0). Furthermore, this network exhibits a remarkable synchronization behaviour in topological scales: the oscillators of high densely interconnected communities synchronize more easily, and more rapidly than the whole network.
基金supported in part by the Program for New Century Excellent Talents in University of China(No.NCET-06-0510)National Natural Science Foundation of China (No. 60874091)the Natural Science Basic Research Project for Universities of Jiangsu Province(No. 08KJD510022)
文摘When complex networks describe a wide range of systems in nature and society,it is increasingly recognized that the topology of real networks are governed by robust organizing principles.Here we discuss the structural metrics such as average path length,clustering coefficient and degree distribution,the main models covering random graphs,small-world and scale-free networks,the interplay between structural properties and the synchronization of complex networks.
基金supported by the National Natural Science Foundation of China(615730176140149961174162)
文摘Multiple complex networks, each with different properties and mutually fused, have the problems that the evolving process is time varying and non-equilibrium, network structures are layered and interlacing, and evolving characteristics are difficult to be measured. On that account, a dynamic evolving model of complex network with fusion nodes and overlap edges(CNFNOEs) is proposed. Firstly, we define some related concepts of CNFNOEs, and analyze the conversion process of fusion relationship and hierarchy relationship. According to the property difference of various nodes and edges, fusion nodes and overlap edges are subsequently split, and then the CNFNOEs is transformed to interlacing layered complex networks(ILCN). Secondly,the node degree saturation and attraction factors are defined. On that basis, the evolution algorithm and the local world evolution model for ILCN are put forward. Moreover, four typical situations of nodes evolution are discussed, and the degree distribution law during evolution is analyzed by means of the mean field method.Numerical simulation results show that nodes unreached degree saturation follow the exponential distribution with an error of no more than 6%; nodes reached degree saturation follow the distribution of their connection capacities with an error of no more than 3%; network weaving coefficients have a positive correlation with the highest probability of new node and initial number of connected edges. The results have verified the feasibility and effectiveness of the model, which provides a new idea and method for exploring CNFNOE's evolving process and law. Also, the model has good application prospects in structure and dynamics research of transportation network, communication network, social contact network,etc.
基金supported by the National Basic Research Program of China (No 2006CB705500)the National Natural Science Foundation of China (Grant Nos 60744003, 10635040, 10532060 and 10472116)the Specialized Research Fund for the Doctoral Program of Higher Education of China
文摘We study the evolutionary snowdrift game in a heterogeneous Newman-Watts small-world network. The heterogeneity of the network is controlled by the number of hubs. It is found that the moderate heterogeneity of the network can promote the cooperation best. Besides, we study how the hubs affect the evolution of cooperative behaviours of the heterogeneous Newman-Watts small-world network. Simulation results show that both the initial states of hubs and the connections between hubs can play an important role. Our work gives a further insight into the effect of hubs on the heterogeneous networks.
文摘We study the congestion phenomenon in a mathematical model of the data packets traffic in transmission networks as a function of the topology and of the load of the network. Two types of traffic are considered: homogeneous and heterogeneous traffic. The congestion phenomenon is studied in stationary conditions through the behaviour of two quantities: the mean travel time of a packet and the mean number of packets that have not reached their destination and are traveling in the network. We define a transformation that maps a network having the small world property (Inet 3037 in our numerical experiments) into a (modified) lattice network that has the same number of nodes. This map changes the capacity of the branches of the graphs representing the networks and can be regarded as an “interpolation” between the two classes of networks. Using this transformation we compare the behaviour of Inet 3037 to the behaviour of a modified rectangular lattice and we study the behaviour of the interpolating networks. This study suggests how to change the network topology and the branch capacities in order to alleviate the congestion phenomenon. In the website: http://www.ceri.uniroma1.it/ceri/zirilli/w6 some auxiliary material including animations and stereo?graphic scenes that helps the understanding of this paper is shown.