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
We study message spreading on a scale-free network, by introducing a novel forget-remember mechanism. Message, a general term which can refer to email, news, rumor or disease, etc, can be forgotten and remembered by i...We study message spreading on a scale-free network, by introducing a novel forget-remember mechanism. Message, a general term which can refer to email, news, rumor or disease, etc, can be forgotten and remembered by its holder. The way the message is forgotten and remembered is governed by the forget and remember function, F and R, respectively. Both F and R are functions of history time t concerrdng individual＇s previous states, namely being active （with message） or inactive （without message）. Our systematic simulations show at the low transmission rate whether or not the spreading can be efficient is primarily determined by the corresponding parameters for F and R.展开更多
It is shown that many real complex networks share distinctive features, such as the small-world effect and the heterogeneous property of connectivity of vertices, which are different from random networks and regular l...It is shown that many real complex networks share distinctive features, such as the small-world effect and the heterogeneous property of connectivity of vertices, which are different from random networks and regular lattices. Although these features capture the important characteristics of complex networks, their applicability depends on the style of networks. To unravel the universal characteristics many complex networks have in common, we study the fractal dimensions of complex networks using the method introduced by Shanker. We find that the average ＇density＇ （p（r ） ） of complex networks follows a better power-law function as a function of distance r with the exponent dl, which is defined as the fractal dimension, in some real complex networks. Furthermore, we study the relation between df and the shortcuts Nadd in small-world networks and the size N in regular lattices. Our present work provides a new perspective to understand the dependence of the fractal dimension df on the complex network structure.展开更多
The air transportation network, one of the common multilayer complex systems, is composed of a collection of individual airlines, and each airline corresponds to a different layer. An important question is then how ma...The air transportation network, one of the common multilayer complex systems, is composed of a collection of individual airlines, and each airline corresponds to a different layer. An important question is then how many airlines are really necessary to represent the optimal structure of a multilayer air transportation system. Here we take the Chinese air transportation network （CATN） as an example to explore the nature of multiplex systems through the procedure of network aggregation. Specifically, we propose a series of structural measures to characterize the CATN from the multilayered to the aggregated network level. We show how these measures evolve during the network aggregation process in which layers are gradually merged together and find that there is an evident structural transition that happened in the aggregated network with nine randomly chosen airlines merged, where the network features and construction cost of this network are almost equivalent to those of the present CATN with twenty-two airlines under this condition. These findings could shed some light on network structure optimization and management of the Chinese air transportation system.展开更多
Many systems can display a very short,rapid changing stage(quasi-discontinuous region)inside a relatively very long and slowly changing process.A quantitative definition for the"quasi-discontinuity"in these ...Many systems can display a very short,rapid changing stage(quasi-discontinuous region)inside a relatively very long and slowly changing process.A quantitative definition for the"quasi-discontinuity"in these systems has been introduced.We have shown by a simplified model that extra-large Feigenbaum constants can be found inside some period-doubling cascades due to the quasi-discontinuity.As an example,this phenomenon has also been observed in Rose-Hindmash model describing neuron activities.展开更多
In a two-dimensional area-preserving map we found a kind of noninvertibility that is induced by a piece-wise smooth property of the map.This can lead to the appearance of such kinds of elliptic islands that attract th...In a two-dimensional area-preserving map we found a kind of noninvertibility that is induced by a piece-wise smooth property of the map.This can lead to the appearance of such kinds of elliptic islands that attract the iterations from a set of initial values outside themselves,while behaving regularly inside.We suggest calling such islands quasi-attractors.展开更多
We propose a model to study the evolution of opinion under the influence of all external field on small world network. The maero-behaviour of agents＇ opinion and the relative change rate as time elapses are studied. ...We propose a model to study the evolution of opinion under the influence of all external field on small world network. The maero-behaviour of agents＇ opinion and the relative change rate as time elapses are studied. The external field is found to play an important role in making the opinion s（t） balance or increase, and without the influence of the external field, the relative change rate γ（t） shows nonlinear increasing behaviour as time runs. What is more, this nonlinear increasing behaviour is independent of the initial condition, the strength of the external field and the time that we cancel the external field. The results may reflect some phenomena in our society, such as the function of the macro-control in China or the mass media in our society.展开更多
We introduce variant rates,for both infection and recovery and noise into the susceptible-infected-removed(SIR)modelfor epidemic spreading.The changing rates are taken mainly due to the changing profiles of an epidemi...We introduce variant rates,for both infection and recovery and noise into the susceptible-infected-removed(SIR)modelfor epidemic spreading.The changing rates are taken mainly due to the changing profiles of an epidemic during its evolution.However,the noise parameter which is taken from a given distribution,i.e.Gaussian can describe the fluctuations of the infection and recovery rates.The numerical simulations show that the SIR model with variant rates and noise and can improve the fitting with real SARS data in the near-stationary stage.展开更多
We present a rigorous method to derive the nonlinear Fokker-Planck （FP） equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang [Chaos, Solitons...We present a rigorous method to derive the nonlinear Fokker-Planck （FP） equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang [Chaos, Solitons ＆ Fractals 23 （2005） 1253] for smooth or quasi-smooth irregular dynamics evolving in Markovian process. The FP equation obtained may take two different but equivalent forms. It was also found that the diffusion constant may depend on both q （the index of Tsallis entropy [J. Stat. Phys. 52 （1988） 479] and the time t.展开更多
A remarkable phenomenon in the time evolution of many networks such as cultural,political,national and economic systems is the recurrent transition between the states of union and the division of nodes.We propose a ph...A remarkable phenomenon in the time evolution of many networks such as cultural,political,national and economic systems is the recurrent transition between the states of union and the division of nodes.We propose a phenomenological modeling,inspired by the maxim"long union divides and long division unites"to investigate the evolutionary characters of these networks composed of the entities whose behaviors are dominated by these two events.The nodes are endowed with quantities such as identity,ingredient,richness(power),openness(connections),age,distance,and interaction,which determine collectively the evolution in a probabilistic way.Depending on a tunable parameter,the time evolution of this model is mainly an alternative domination of union or division state,with a possible state of final union dominated by one single node.展开更多
Different types of models for describing the motion of a kicked ion were suggested and studied. It is shown that certain kinds of jumping behavior of the exerting electromagnetic field can lead to a type of noninverti...Different types of models for describing the motion of a kicked ion were suggested and studied. It is shown that certain kinds of jumping behavior of the exerting electromagnetic field can lead to a type of noninvertible property, which changes this conservative system into a 'quasi-dissipative' one. The quasi-dissipative behaviors allow the particle to move along a confined chaotic 'quasi-attractor' in many regions of the parameter space. If the exerting electromagnetic field is discontinuous but the system is still invertible, it will take an unbounded chaotic diffusion with similar parameter values. We hope that this discovery could provide a helpful idea for confining the plasma.展开更多
Livestock transportation is a key factor that contributes to the spatial spread of brucellosis.To analyze the impact of sheep transportation on brucellosis transmission,we develop a human–sheep coupled brucellosis mo...Livestock transportation is a key factor that contributes to the spatial spread of brucellosis.To analyze the impact of sheep transportation on brucellosis transmission,we develop a human–sheep coupled brucellosis model within a metapopulation network framework.Theoretically,we examine the positively invariant set,the basic reproduction number,the existence,uniqueness,and stability of disease-free equilibrium and the existence of the endemic equilibrium of the model.For practical application,using Heilongjiang province as a case study,we simulate brucellosis transmission across 12 cities based on data using three network types:the BA network,the ER network,and homogeneous mixing network.The simulation results indicate that the network's average degree plays a role in the spread of brucellosis.For BA and ER networks,the basic reproduction number and cumulative incidence of brucellosis stabilize when the network's average degree reaches 4 or 5.In contrast,sheep transport in a homogeneous mixing network accelerates the cross-regional spread of brucellosis,whereas transportation in a BA network helps to control it effectively.Furthermore,the findings suggest that the movement of sheep is not always detrimental to controlling the spread of brucellosis.For cities with smaller sheep populations,such as Shuangyashan and Qitaihe,increasing the transport of sheep outward amplifies the spatial spread of the disease.In contrast,in cities with larger sheep populations,such as Qiqihar,Daqing,and Suihua,moderate sheep outflow can help reduce the spread.In addition,cities with large livestock populations play a dominant role in the overall transmission dynamics,underscoring the need for stricter supervision in these areas.展开更多
Ecotechnology,quintessential for crafting sustainable socio-environmental strategies,remains tantalizingly uncharted.Our analysis,steered by the nuances of machine learning and augmented by bibliometric insights,delin...Ecotechnology,quintessential for crafting sustainable socio-environmental strategies,remains tantalizingly uncharted.Our analysis,steered by the nuances of machine learning and augmented by bibliometric insights,delineates the expansive terrain of this domain,elucidates pivotal research themes and conundrums,and discerns the vanguard nations in this field.Furthermore,we deftly connect our discoveries to the United Nations'2030 Sustainable Development Goals,thereby accentuating the profound societal ramifications of ecotechnology.展开更多
<Abstract>English and Chinese language frequency time series (LFTS) were constructed based on an English and two Chinese novels. Methods of statistical hypothesis testing were adopted to test the nonlinear prope...<Abstract>English and Chinese language frequency time series (LFTS) were constructed based on an English and two Chinese novels. Methods of statistical hypothesis testing were adopted to test the nonlinear properties of the LFTS. Results suggest the series exhibited non-normal, auto-correlative, and stationary characteristics. Moreover, we found that LFTS follow the power law distributions, and thereby we investigated the fractal structure, long range correlation, and intermittency, which indicated the self-similarity features of LFTS, and also provided hints that human societies are likely to share some universal properties.展开更多
A first-principles derivation is presented of canonical distributions for a finite thermostat taking into account nonextensive energy. Parameterizing this energy by λ , we derive an explicit form for the distribution...A first-principles derivation is presented of canonical distributions for a finite thermostat taking into account nonextensive energy. Parameterizing this energy by λ , we derive an explicit form for the distribution functions by regulating λ , and then explore the nontrivial relationship between these functions and energy nonextensivity, as well other system parameters such as system size. A variational entropy function is also derived from these distribution functions.展开更多
Two kinds of noise strategies in binary opinion dynamics on ER random networks are discussed. Random noise p1 in the initial configuration plays a role in redistributing the opinion states associated with the network....Two kinds of noise strategies in binary opinion dynamics on ER random networks are discussed. Random noise p1 in the initial configuration plays a role in redistributing the opinion states associated with the network. Under synchronous updating, the system can attain a stable state within few time steps. The fraction of nodes with changed opinion states F decreases exponentially with time, and the ratio of one of the two opinion states R remains almost unchanged during the evolution. The average ratio <R> crosses at the half-half initial concentration under different p1. For noise in the dynamical evolution p2, the system can reach a steady state with small fluctuations. With larger p2, more nodes have changed opinion states at each updating and more nodes with opposite opinions coexist. If p2 is greater than 0.5, the two opinions coexist with equal support.展开更多
We propose a mean-field Bak-Sneppen (MFBS) model with varying interaction strength. The interaction strength, here denoted by α, specifies the degree of interaction, and varies smoothly between 0 for no interaction a...We propose a mean-field Bak-Sneppen (MFBS) model with varying interaction strength. The interaction strength, here denoted by α, specifies the degree of interaction, and varies smoothly between 0 for no interaction and 1 for full interaction (restoring the original BS model). Our simulations of the MFBS model reveal some interesting features. When α is non-zero, the MFBS model can evolve to a self-organized critical (SOC) state. The critical exponent of the avalanche size distribution, α, is insensitive to changes in α. The critical exponent of average avalanche size, α, and the avalanche dimension exponent, D, both increase slightly with α < 0.5 but remain constant if α > 0.5. The critical threshold fc decreases almost linearly with α.展开更多
We construct a weighted network of scientific collaboration in computational geometry and study the statistical properties of the network. In addition, we introduce a parameter called the collaboration relationship pa...We construct a weighted network of scientific collaboration in computational geometry and study the statistical properties of the network. In addition, we introduce a parameter called the collaboration relationship parameter to measure the collaboration between scientists. The collaboration relationship parameter of two scientists depends not only on the connection weights between the nodes, but also on the network's structure. The stability of the network's structure in terms of different edge removal strategies is also studied. According to the parameter, we find that a community structure exists in this type of network.展开更多
The society structure plays an important role in shaping the attitudes,beliefs and public opinion.For studying the role of the society structure in opinion dynamics,we analyze the Sznajd model on small-world network f...The society structure plays an important role in shaping the attitudes,beliefs and public opinion.For studying the role of the society structure in opinion dynamics,we analyze the Sznajd model on small-world network formed by adding shortcuts in a lattice consisting of N nodes arranged in a ring and on two-dimensional(2-D)regular lattice.Through computer simulation,we find that there exists a pseudo-phase transition from the coexistence state forφ<φ_(c) to the consensus state forφ>φ_(c),whereφ_(c) is some threshold for the shortcut densityφ,which is dependent of the complex network topology and the dimensionality of complex networks.Our observations indicate the dependence of the opinion dynamics on the complex system topology.展开更多
In this paper,we propose a simple model of opinion dynamics to construct social networks,based on the algorithm of link rewiring of local attachment(RLA)and global attachment(RGA).Generality,the system does reach a st...In this paper,we propose a simple model of opinion dynamics to construct social networks,based on the algorithm of link rewiring of local attachment(RLA)and global attachment(RGA).Generality,the system does reach a steady state where all individuals'opinion and the complex network structure are fixed.The RGA enhances the ability of consensus of opinion formation.Furthermore,by tuning a model parameter p,which governs the proportion of RLA and RGA,we find the formation of hierarchical structure in the social networks for p>p_(c).Here,p_(c) is related to the complex network size N and the minimal coordination number 2K.The model also reproduces many features of large social networks,including the“weak links”property.展开更多
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 in part by the National Natural Science Foundation of China under Grant Nos 70401020, 70571027, 10647125 and 10635020, and the Ministry of Education of China under Grant No 306022, and the 111 Project under Grant No B08033.
文摘We study message spreading on a scale-free network, by introducing a novel forget-remember mechanism. Message, a general term which can refer to email, news, rumor or disease, etc, can be forgotten and remembered by its holder. The way the message is forgotten and remembered is governed by the forget and remember function, F and R, respectively. Both F and R are functions of history time t concerrdng individual＇s previous states, namely being active （with message） or inactive （without message）. Our systematic simulations show at the low transmission rate whether or not the spreading can be efficient is primarily determined by the corresponding parameters for F and R.
基金Supported by the National Natural Science Foundation of China under Grant No 10635020,the Program of Introducing Talents of Discipline to Universities under Grant No B08033, the National Key Basic Research Program of China under Grant No 2008CB317106, and the Key Project of the Ministry of Education of China （306022 and IRT0624）.
文摘It is shown that many real complex networks share distinctive features, such as the small-world effect and the heterogeneous property of connectivity of vertices, which are different from random networks and regular lattices. Although these features capture the important characteristics of complex networks, their applicability depends on the style of networks. To unravel the universal characteristics many complex networks have in common, we study the fractal dimensions of complex networks using the method introduced by Shanker. We find that the average ＇density＇ （p（r ） ） of complex networks follows a better power-law function as a function of distance r with the exponent dl, which is defined as the fractal dimension, in some real complex networks. Furthermore, we study the relation between df and the shortcuts Nadd in small-world networks and the size N in regular lattices. Our present work provides a new perspective to understand the dependence of the fractal dimension df on the complex network structure.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11405118,11401448 and 11301403
文摘The air transportation network, one of the common multilayer complex systems, is composed of a collection of individual airlines, and each airline corresponds to a different layer. An important question is then how many airlines are really necessary to represent the optimal structure of a multilayer air transportation system. Here we take the Chinese air transportation network （CATN） as an example to explore the nature of multiplex systems through the procedure of network aggregation. Specifically, we propose a series of structural measures to characterize the CATN from the multilayered to the aggregated network level. We show how these measures evolve during the network aggregation process in which layers are gradually merged together and find that there is an evident structural transition that happened in the aggregated network with nine randomly chosen airlines merged, where the network features and construction cost of this network are almost equivalent to those of the present CATN with twenty-two airlines under this condition. These findings could shed some light on network structure optimization and management of the Chinese air transportation system.
基金Supported by the National Natural Science Foundation of China under Grant No.19975039the Foundation of Jiangsu Provincial Education Committee under the Grant No.98kjb140006.
文摘Many systems can display a very short,rapid changing stage(quasi-discontinuous region)inside a relatively very long and slowly changing process.A quantitative definition for the"quasi-discontinuity"in these systems has been introduced.We have shown by a simplified model that extra-large Feigenbaum constants can be found inside some period-doubling cascades due to the quasi-discontinuity.As an example,this phenomenon has also been observed in Rose-Hindmash model describing neuron activities.
基金Supported by the National Natural Science Foundation of China under Grant Nos.19975039,49474216 and 59876093the Natural Science Foundation of Jiangsu Provincial Education Committee under Grant No.98kjb140006the Chinese National Basic Research Climbing Project.
文摘In a two-dimensional area-preserving map we found a kind of noninvertibility that is induced by a piece-wise smooth property of the map.This can lead to the appearance of such kinds of elliptic islands that attract the iterations from a set of initial values outside themselves,while behaving regularly inside.We suggest calling such islands quasi-attractors.
基金Supported by the National Natural Science Foundation of China under grant Nos 70571027, 70401020, 10647125 and 10635020, and the Ministry of Education of China under Grant No 306022.
文摘We propose a model to study the evolution of opinion under the influence of all external field on small world network. The maero-behaviour of agents＇ opinion and the relative change rate as time elapses are studied. The external field is found to play an important role in making the opinion s（t） balance or increase, and without the influence of the external field, the relative change rate γ（t） shows nonlinear increasing behaviour as time runs. What is more, this nonlinear increasing behaviour is independent of the initial condition, the strength of the external field and the time that we cancel the external field. The results may reflect some phenomena in our society, such as the function of the macro-control in China or the mass media in our society.
基金Supported in part by the National Natural Science Foundation of China under Grant Nos 10647125,10635020,10975057 and 10975062the Program of Introducing Talents of Discipline to Universities under Grant No B08033.GU Jiao is supported by Max-Planck-Institute for Mathematics in the Sciences。
文摘We introduce variant rates,for both infection and recovery and noise into the susceptible-infected-removed(SIR)modelfor epidemic spreading.The changing rates are taken mainly due to the changing profiles of an epidemic during its evolution.However,the noise parameter which is taken from a given distribution,i.e.Gaussian can describe the fluctuations of the infection and recovery rates.The numerical simulations show that the SIR model with variant rates and noise and can improve the fitting with real SARS data in the near-stationary stage.
基金Supported by the National Natural Science Foundation of China under Grant Nos 70401020, 70571027, 10647125, and 10635020, and the Ministry of Education of China under Grant No 306022.
文摘We present a rigorous method to derive the nonlinear Fokker-Planck （FP） equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang [Chaos, Solitons ＆ Fractals 23 （2005） 1253] for smooth or quasi-smooth irregular dynamics evolving in Markovian process. The FP equation obtained may take two different but equivalent forms. It was also found that the diffusion constant may depend on both q （the index of Tsallis entropy [J. Stat. Phys. 52 （1988） 479] and the time t.
文摘A remarkable phenomenon in the time evolution of many networks such as cultural,political,national and economic systems is the recurrent transition between the states of union and the division of nodes.We propose a phenomenological modeling,inspired by the maxim"long union divides and long division unites"to investigate the evolutionary characters of these networks composed of the entities whose behaviors are dominated by these two events.The nodes are endowed with quantities such as identity,ingredient,richness(power),openness(connections),age,distance,and interaction,which determine collectively the evolution in a probabilistic way.Depending on a tunable parameter,the time evolution of this model is mainly an alternative domination of union or division state,with a possible state of final union dominated by one single node.
基金the National Natural Foundation of China under Grant No. 19975039.
文摘Different types of models for describing the motion of a kicked ion were suggested and studied. It is shown that certain kinds of jumping behavior of the exerting electromagnetic field can lead to a type of noninvertible property, which changes this conservative system into a 'quasi-dissipative' one. The quasi-dissipative behaviors allow the particle to move along a confined chaotic 'quasi-attractor' in many regions of the parameter space. If the exerting electromagnetic field is discontinuous but the system is still invertible, it will take an unbounded chaotic diffusion with similar parameter values. We hope that this discovery could provide a helpful idea for confining the plasma.
基金Project supported by the National Natural Science Foundation of China(Grant No.12101443,12371493)the Natural Science Foundation of Shanxi Province(Grant Nos.20210302124260 and 202303021221024)。
文摘Livestock transportation is a key factor that contributes to the spatial spread of brucellosis.To analyze the impact of sheep transportation on brucellosis transmission,we develop a human–sheep coupled brucellosis model within a metapopulation network framework.Theoretically,we examine the positively invariant set,the basic reproduction number,the existence,uniqueness,and stability of disease-free equilibrium and the existence of the endemic equilibrium of the model.For practical application,using Heilongjiang province as a case study,we simulate brucellosis transmission across 12 cities based on data using three network types:the BA network,the ER network,and homogeneous mixing network.The simulation results indicate that the network's average degree plays a role in the spread of brucellosis.For BA and ER networks,the basic reproduction number and cumulative incidence of brucellosis stabilize when the network's average degree reaches 4 or 5.In contrast,sheep transport in a homogeneous mixing network accelerates the cross-regional spread of brucellosis,whereas transportation in a BA network helps to control it effectively.Furthermore,the findings suggest that the movement of sheep is not always detrimental to controlling the spread of brucellosis.For cities with smaller sheep populations,such as Shuangyashan and Qitaihe,increasing the transport of sheep outward amplifies the spatial spread of the disease.In contrast,in cities with larger sheep populations,such as Qiqihar,Daqing,and Suihua,moderate sheep outflow can help reduce the spread.In addition,cities with large livestock populations play a dominant role in the overall transmission dynamics,underscoring the need for stricter supervision in these areas.
基金.Ricardo Ruíz-Sanchez was partially supported by the UNAM-DGAPA postdoctoral fellowship program。
文摘Ecotechnology,quintessential for crafting sustainable socio-environmental strategies,remains tantalizingly uncharted.Our analysis,steered by the nuances of machine learning and augmented by bibliometric insights,delineates the expansive terrain of this domain,elucidates pivotal research themes and conundrums,and discerns the vanguard nations in this field.Furthermore,we deftly connect our discoveries to the United Nations'2030 Sustainable Development Goals,thereby accentuating the profound societal ramifications of ecotechnology.
基金supported by the National Natural Science Foundation of China (10647125, 10635020, 10975057 and 10975062)the Program of Introducing Talents of Discipline to Universities (B08033)the PHC CAI YUAN PEI Program (LIU JIN OU [2010] No. 6050) (2010008104)
文摘<Abstract>English and Chinese language frequency time series (LFTS) were constructed based on an English and two Chinese novels. Methods of statistical hypothesis testing were adopted to test the nonlinear properties of the LFTS. Results suggest the series exhibited non-normal, auto-correlative, and stationary characteristics. Moreover, we found that LFTS follow the power law distributions, and thereby we investigated the fractal structure, long range correlation, and intermittency, which indicated the self-similarity features of LFTS, and also provided hints that human societies are likely to share some universal properties.
基金supported by the National Natural Science Foundation of China (10647125, 10635020, 10975057, 10975062)the Program of Introducing Talents of Discipline to Universities (B08033)
文摘A first-principles derivation is presented of canonical distributions for a finite thermostat taking into account nonextensive energy. Parameterizing this energy by λ , we derive an explicit form for the distribution functions by regulating λ , and then explore the nontrivial relationship between these functions and energy nonextensivity, as well other system parameters such as system size. A variational entropy function is also derived from these distribution functions.
基金supported in part by the National Natural Science Founda-tion of China (10635020 and 10975057)the Ministry of Education of China (306022)
文摘Two kinds of noise strategies in binary opinion dynamics on ER random networks are discussed. Random noise p1 in the initial configuration plays a role in redistributing the opinion states associated with the network. Under synchronous updating, the system can attain a stable state within few time steps. The fraction of nodes with changed opinion states F decreases exponentially with time, and the ratio of one of the two opinion states R remains almost unchanged during the evolution. The average ratio <R> crosses at the half-half initial concentration under different p1. For noise in the dynamical evolution p2, the system can reach a steady state with small fluctuations. With larger p2, more nodes have changed opinion states at each updating and more nodes with opposite opinions coexist. If p2 is greater than 0.5, the two opinions coexist with equal support.
基金supported by the National Natural Science Foundation of China (10647125, 10635020, 10975057 and 10975062)the Program of Introducing Talents of Discipline to Universities (B08033)the Max-Planck-Institute for Mathematics in the Sciences
文摘We propose a mean-field Bak-Sneppen (MFBS) model with varying interaction strength. The interaction strength, here denoted by α, specifies the degree of interaction, and varies smoothly between 0 for no interaction and 1 for full interaction (restoring the original BS model). Our simulations of the MFBS model reveal some interesting features. When α is non-zero, the MFBS model can evolve to a self-organized critical (SOC) state. The critical exponent of the avalanche size distribution, α, is insensitive to changes in α. The critical exponent of average avalanche size, α, and the avalanche dimension exponent, D, both increase slightly with α < 0.5 but remain constant if α > 0.5. The critical threshold fc decreases almost linearly with α.
基金supported by the National Natural Science Foundation of China (10647125, 10635020, 10975057 and 10975062)the Program of Introducing Talents of Discipline to Universities (B08033)the PHC CAI YUAN PEI Program (LIU JIN OU [2010] No. 6050)
文摘We construct a weighted network of scientific collaboration in computational geometry and study the statistical properties of the network. In addition, we introduce a parameter called the collaboration relationship parameter to measure the collaboration between scientists. The collaboration relationship parameter of two scientists depends not only on the connection weights between the nodes, but also on the network's structure. The stability of the network's structure in terms of different edge removal strategies is also studied. According to the parameter, we find that a community structure exists in this type of network.
基金This work was Supported by the NSFC(10635020)the Programme of Introducing Talents of Discipline to Universities under Grant No.B08033+1 种基金the State Key Development Program of Basic Research of China(2008CB317106)the Key Project of Chinese Ministry of Education(306022 and IRT0624).
文摘The society structure plays an important role in shaping the attitudes,beliefs and public opinion.For studying the role of the society structure in opinion dynamics,we analyze the Sznajd model on small-world network formed by adding shortcuts in a lattice consisting of N nodes arranged in a ring and on two-dimensional(2-D)regular lattice.Through computer simulation,we find that there exists a pseudo-phase transition from the coexistence state forφ<φ_(c) to the consensus state forφ>φ_(c),whereφ_(c) is some threshold for the shortcut densityφ,which is dependent of the complex network topology and the dimensionality of complex networks.Our observations indicate the dependence of the opinion dynamics on the complex system topology.
基金supported by the National Natural Science Foundation of China(Grant Nos.10647125,10635020,10975057 and 10975062)the Programme of Introducing Talents of Discipline to Universities under Grant No.B08033.
文摘In this paper,we propose a simple model of opinion dynamics to construct social networks,based on the algorithm of link rewiring of local attachment(RLA)and global attachment(RGA).Generality,the system does reach a steady state where all individuals'opinion and the complex network structure are fixed.The RGA enhances the ability of consensus of opinion formation.Furthermore,by tuning a model parameter p,which governs the proportion of RLA and RGA,we find the formation of hierarchical structure in the social networks for p>p_(c).Here,p_(c) is related to the complex network size N and the minimal coordination number 2K.The model also reproduces many features of large social networks,including the“weak links”property.
