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We propose a nonlinear voter model to study the emergence of global consensus in opinion dynamics. In our model, agent i agrees with one of binary opinions with the probability that is a power function of the number of agents holding this opinion among agent i and its nearest neighbors, where an adjustable parameter α controls the effect of herd behavior on consensus. We find that there exists an optimal value of α leading to the fastest consensus for lattices, random graphs, small-world networks and scale-free networks. Qualitative insights are obtained by examining the spatiotemporal evolution of the opinion clusters.

Using the cellular automaton traffic flow model, we investigate an unsignalized intersection which consists of two perpendicular one-lane roads. Both the roads cross at a point and the intersecting roads are cyclic. Each vehicle may pass or occupy the intersection where all the vehicles on both roads are not allowed to turn. Different from Ishibashi and Fukui’s studies in which the update is carried out for both roads in turn, the parallel update is proposed and its detailed rules are presented in our model. In this work, the cases of different maximum vehicle velocities on both roads are considered. Based on simulation results and the principle for constructing phase diagrams, phase diagrams are mapped out and their specific flow formulas for all the regions in the phase diagrams are obtained for various vehicle densities, which are seldom done in previous studies. One also finds that the topology of phase diagrams depends on the update rules of eastbound and northbound roads and their maximum velocities of vehicles.

The road capacity can be greatly improved if an appropriate and effective information feedback strategy is adopted in the traffic system. In this paper, a strategy called piecewise function feedback strategy (PFFS) is introduced and applied into an asymmetrical two-route scenario with a speed limit bottleneck in which the dynamic information can be generated and displayed on the information board to guide road users to make a choice. Meanwhile, the velocity-dependent randomization (VDR) mechanism is adopted which can better reflect the dynamic behavior of vehicles in the system than NS mechanism. Simulation results adopting PFFS have demonstrated high efficiency in controlling spatial distribution of traffic patterns compared with the previous strategies.

This Letter investigates a totally asymmetric simple exclusion process (TASEP) with junctions in a one-dimensional transport system. Parallel update rules and periodic boundary condition are adopted. Two cases corresponding to different update rules are studied. The results show that the stationary states of system mainly depend on the selection behavior of particle at the bifurcation point.

Traffic jam has become a big problem in the development of economy. How to effectively improve the road capacity is becoming the key problem in the research of traffic flow. As the core part of the next generation intelligent transportation systems, the feedback strategy has attracted much attention. In recent years, researchers have proposed many effective strategies. In this paper, a strategy called speed of last vehicle feedback strategy is introduced, and simulated in a two-route scenario with one exit. Result shows that compared with other strategies, this strategy has certain advantages on average flux — a criteria describing traffic capacity of traffic systems. More importantly, the implementation of this strategy is very simple.

Usually, whether to take vaccination or not is a voluntary decision, which is determined by many factors, from societal factors (such as religious belief and human rights) to individual preferences (including psychology and altruism). Facing the outbreaks of infectious diseases, different people often have different estimations on the risk of infectious diseases. So, some persons are willing to vaccinate, but other persons are willing to take risks. In this paper, we establish two different risk assessment systems using the technique of dynamic programming, and then compare the effects of the two different systems on the prevention of diseases on complex networks. One is that the perceived probability of being infected for each individual is the same (uniform case). The other is that the perceived probability of being infected is positively correlated to individual degrees (preferential case). We show that these two risk assessment systems can yield completely different results, such as, the effectiveness of controlling diseases, the time evolution of the number of infections, and so on., Research highlights ► On an outbreak of an infectious disease, individual decisions on vaccination depend on whether they can accurately estimate the risk of the disease. ► So, in this work, we establish two different risk assessment systems using the technique of dynamic programming. By comparing the two different risk assessment systems, we find that how individuals estimate the risk of infection determines the effectiveness of control strategy. ► Furthermore, many other interesting results are enclosed in this work.

In this paper, the delay probability of the original Nagel and Schreckenberg model is modified to simulate one-lane traffic flow. The delay probability of a vehicle depends on its corresponding gap. According to simulation results, it has been found that the structure of the fundamental diagram of the new model is sensitively dependent on the values of the delay probability. In comparison with the NS model, one notes that the fundamental diagram of the new model is more consistent with the results measured in the real traffic, and the velocity distributions of the new model are relatively reasonable.

In this paper, we investigate two two-route traffic models, i.e. asymmetric and symmetric two-route traffic models, with mean velocity information feedback strategy. The simulation results show that, for asymmetric two-route model, average flux can be significantly improved if only partial road information is provided for road users. However, for symmetric two-route model, average flux of the two routes adopting information feedback cannot outweigh the flux of two routes chosen completely at random. We explain the results by studying the vehicle number on two routes. We hope the study may provide a good suggestion to the design of Advanced Traveler Information Systems.

We propose a negotiation strategy to address the effect of geography on the dynamics of naming games over small-world networks. Communication and negotiation frequencies between two agents are determined by their geographical distance in terms of a parameter characterizing the correlation between interaction strength and the distance. A finding is that there exists an optimal parameter value leading to fastest convergence to global consensus on naming. Numerical computations and a theoretical analysis are provided to substantiate our findings.

In this paper, we study an aspiration-induced migration model, in which each individual plays the prisoner’s dilemma game with those being within a circle of radius r centered on himself/herself. An individual will migrate to a randomly chosen place with the velocity v if his/her payoff is below the aspiration level. We report that cooperative behavior is favored when the aspiration level and interaction radius are moderate, and the migration velocity is slow.

Heritability is ubiquitous within most real biological or social systems. A heritable trait is most simply an offspring’s trait that resembles the parent’s corresponding trait, which can be fitness, strategy, or the way of strategy adoption for evolutionary games. Here we study the effects of heritability on the evolution of spatial public goods games. In our model, the fitness of players is determined by the payoffs from the current interactions and their history. Based on extensive simulations, we find that the density of cooperators is enhanced by increasing the heritability of players over a wide range of the multiplication factor. We attribute the enhancement of cooperation to the inherited fitness that stabilizes the fitness of players, and thus prevents the expansion of defectors effectively.

An evolutionary prisoner’s dilemma game with players adjusting their learning motivation is studied. At each time step, each player can adjust his/her learning motivation according to the difference between the current payoff and payoff aspiration. Greater payoff aspiration means stronger learning motivation, and vice versa. We find that the density of cooperation in a spatial prisoner’s dilemma game is enhanced when the learning motivation mechanism is considered. Meanwhile, we show that proper noise can not only induce the highest cooperation level but also can maintain the cooperation phenomenon even though there is more temptation to defect.

Based on the Ishibashi and Fukui crossroad traffic flow model [Y. Ishibashi and M. Fukui. J. Phys. Soc. Japan. 70 (2001) 2793], mixed traffic flow (i.e., the fast and slow vehicles with different maximum velocities are mixed) is investigated in this work. According to the numerical simulation results and the principle for constructing the phase diagram, phase diagrams for mixed traffic flow are constructed. It is noted that the topology of these phase diagrams is similar to that of phase diagrams for homogeneous vehicles (which refers to slow vehicles only). From the phase diagrams, it is evident that mixed traffic flow is influenced by the mixing rate f (fraction of slow and fast vehicles) in regions II and V, but not in other regions. Although a mixture of fast and slow vehicles is introduced in the crossroad traffic flow model, the separation between phases in the phase diagrams remains linear. For a given q (the vehicle density on the northbound road), one flow plateau appears in regions IIx or IVy, while two maximum flow plateaus appear in region V in each of the phase diagrams. The maximum flow values in region V reflect the maximum traffic capacity for the traffic system as defined in this work. Since mixed traffic flow is a common phenomenon in real traffic, this work may offer help in real traffic simulations and traffic management.

In this brief report, we investigate the synchronizability of the complex network. In order to optimize the synchronizability, we propose a method by introducing a weight matrix, which makes the synchronized states stable for the widest range of the overall coupling strength. We give a proof in mathematics and gain the exact form of the weight matrix, which is equal to Lβ. Matrix L is the one that describes the optimal network and matrix β is constructed by the eigenvalues and eigenvectors of the usual Laplacian matrix. This result may provide us insight into the synchronization of complex network more deeply.

The optimal information feedback has a significant effect on many socioeconomic systems like stock market and traffic systems aiming to make full use of resources. In this paper, we study dynamics of traffic flow with real-time information. The influence of a feedback strategy named vehicle number feedback strategy (VNFS) is introduced, in which we only calculate the vehicle number of first 500 route sites from the entrance. Moreover, the two-route traffic system has only one entrance and one exit, which is different from those in the previous work. Our model incorporates the effects of adaptability into the cellular automaton models of traffic flow, and simulation results by adopting this optimal information feedback strategy have demonstrated higher efficiency in controlling spatial distribution of traffic patterns than the other three information feedback strategies, i.e., TTFS, MVFS and CCFS.

Under the assumption that the decision of vaccination is a voluntary behavior, in this paper, we use two forms of risk functions to characterize how susceptible individuals estimate the perceived risk of infection. One is uniform case, where each susceptible individual estimates the perceived risk of infection only based on the density of infection at each time step, so the risk function is only a function of the density of infection; another is preferential case, where each susceptible individual estimates the perceived risk of infection not only based on the density of infection but only related to its own activities/immediate neighbors (in network terminology, the activity or the number of immediate neighbors is the degree of node), so the risk function is a function of the density of infection and the degree of individuals. By investigating two different ways of estimating the risk of infection for susceptible individuals on complex network, we find that, for the preferential case, the spread of epidemic can be effectively controlled; yet, for the uniform case, voluntary vaccination mechanism is almost invalid in controlling the spread of epidemic on networks. Furthermore, given the temporality of some vaccines, the waves of epidemic for two cases are also different. Therefore, our work insight that the way of estimating the perceived risk of infection determines the decision on vaccination options, and then determines the success or failure of control strategy.

To research the statistical properties of human’s communication behaviors is one of the highlight areas of Human Dynamics. In this paper, we analyze the instant message data of QICQ from volunteers, and discover that there are many forms of non-Poisson characters, such as inter-event distributions of sending and receiving messages, communications between two friends, log-in activities, the distribution of online time, quantities of messages, and so on. These distributions not only denote the pattern of human communication activities, but also relate to the statistical property of human behaviors in using software. We find out that most of these exponents distribute between −1 and −2, which indicates that the Instant Message (IM) communication behavior of human is different from Non-IM communication behaviors; there are many fat-tail characters related to IM communication behavior.

We first study the influence of an efficient feedback strategy named prediction feedback strategy (PFS) based on a multi-route scenario in which dynamic information can be generated and displayed on the board to guide road users to make a choice. In this scenario, our model incorporates the effects of adaptability into the cellular automaton models of traffic flow. Simulation results adopting this optimal information feedback strategy have demonstrated high efficiency in controlling spatial distribution of traffic patterns compared with the other three information feedback strategies, i.e., vehicle number and flux. At the end of this paper, we also discuss in what situation PFS will become invalid in multi-route systems., 15 pages, 15 figures, Physica A (2010), doi:10.1016/j.physa.2010.02.036

We propose an opinion dynamics model to study the effects of heterogeneous influence of individuals on the global consensus. Each individual is assigned a weight that is proportional to the power of its degree, where the power exponent α is an adjustable parameter. Interestingly, it is found that there exists an optimal value of α leading to the shortest consensus time for scale-free networks, random networks and small-world networks. Other quantities, such as the probability that an individual's initial opinion becomes the final opinion as a function of degree, the evolution of the number of opinion clusters, as well as the relationship between average consensus time and the network size, are also studied. Our results are helpful for understanding the role of heterogeneous influence in the opinion dynamics.

In this paper, we propose a novel dynamical task-based model to investigate the origin of non-Poisson properties in human mobility pattern. Considering the distance and the memory effects in the decision of human travel, our model simulates the walking process of a walker in a two dimension square landscape. In the walking process, the nearer and more familiar places usually have more possible to be chosen as the aim location of travel. Simulation results indicate that our model can generate not only the power-law displacement distribution, but also the localization property and non-homogeneous visiting frequency distribution. These results in agreement most of conclusions of the empirical statistics, imply the impacts of distance and memory are important in the emergence of non-Poisson property in human mobility pattern.

In this paper, we present a recommendation algorithm based on the resource-allocation progresses on bipartite networks. In this model, each node is assigned an attraction that is proportional to the power of its degree, where the exponent β is an adjustable parameter that controls the configuration of attractions. In the resource-allocation process, each transmitter distributes its each neighbor a fragment of resource that is proportional to the attraction of the neighbor. Based on a benchmark database, we find that decreasing the attractions that the nodes with higher degrees are assigned can further improve the algorithmic accuracy. More significantly, numerical results show that the optimal configuration of attractions subject to accuracy can also generate more diverse and less popular recommendations.

The study of the spread of epidemic on different social networks has attracted many attentions from researchers in different fields. One main topical problem is the threshold of transmission rate or the basic reproductive number on different social networks. Recently, several efficient methods on solving the threshold of epidemic on heterogeneous networks were proposed. In this paper, we summarize several methods and compare their advantages or disadvantages systematically.

We study the effects of heritability on the evolution of the spatial prisoner’s dilemma game. In our model, the fitness of each player is composed of the instantaneous payoff from the interactions and the inherited fitness from the last generation. Based on extensive simulations, we find that the density of cooperators is enhanced by increasing the heritability of players over a wide range of the model parameter. The mean fitness of cooperators and defectors are also studied for understanding our results.

We first study dynamics of traffic flow with real-time information and the influence of a new feedback strategy named Vehicle Number Feedback Strategy (VNFS) in a multi-route scenario in which dynamic information can be generated and displayed on the board (the board refers to a variable message sign where information on the routes is displayed) to guide road users to make a choice. In a multi-route scenario, our model incorporates the effects of adaptability into the cellular automaton models of traffic flow and simulation results adopting vehicle number feedback strategy have demonstrated high efficiency in controlling spatial distribution of traffic patterns compared with the other three information feedback strategies, i.e. Travel Time Feedback Strategy (TTFS), Mean Velocity Feedback Strategy (MVFS) and Congestion Coefficient Feedback Strategy (CCFS). We also discuss the influence of expected arrival rate (Vp) at the entrance on the average flux of each route, and we find that the flux adopting VNFS is always the largest at each Vp value among these four feedback strategies.

We study the role of social diversity in the evolutionary game and opinion dynamics on scale-free networks. Each individual is assigned a weight that is proportional to the power of its degree, where the exponent α is an adjustable parameter that controls the level of diversity among individuals in the network. It is found that there exists an optimal value of α , leading to the highest cooperation level or the fastest consensus. We give some qualitative explanations for the emergence of optimal α .

As a killing machine and a decisive factor of history, wars play an important role in social system. In this paper, we present an empirical exploration of the distribution of recurrent time of wars in ancient China and find that it obeys a stretched exponential form. The pattern we found implies that there are undetected mechanisms that underlie the dynamics of wars. In order to explain the origin of this form, a model mainly based on the correlation between two consecutive wars is constructed, which is somewhat similar to the Bak–Sneppen model. The simulation results of the model are in agreement with the empirical statistics and suggest that the dynamics of wars could relate with self-organized criticality.

Most previous studies on the synchronization of complex networks were based on that each node managed to adjust its neighbors coupling strength to enhance synchronizability, i.e. each node tried to adjust its total input coupling strength in a proper way and the neighbor nodes were passively adjusted. From practical and engineering viewpoints, each node should manage to adjust its total output coupling strength to realize synchronization. Moreover, each node's total output coupling strength can be distributed to its neighbors with different proportions. In view of the above reasons, in this paper, we study the synchronization of complex networks under the assumptions that the total output coupling strength of each node is voluntarily/directly distributed to its neighbors with different proportions. What is more, we assume that the total output coupling strength of each node can be nonlinear to its degree. Our analysis and numerical simulations show that the synchronizability can be enhanced dramatically when the parameters are properly selected.

In this paper, traffic bottleneck is introduced on one of the routes (say route A) in a two-route scenario with mean velocity information feedback. The simulations show that four different system states, i.e. zero state (no dynamic vehicle chooses route A), periodic oscillation state (mean velocity on route A is in periodic oscillations), alternation state (alternation of zero state and oscillation state), and equal velocity state (mean velocities on the two routes are equal), are identified. Complex nonlinear changing behavior of critical vehicle arrival probability λcdepending on bottleneck length and location as well as dynamic vehicle ratio is revealed. Our work is expected to be useful for designing Advanced Traveller Information Systems.

In this paper, we bring an unequal payoff allocation mechanism into evolutionary public goods game on scale-free networks and focus on the cooperative behavior of the system. The unequal mechanism can be tuned by one parameter α : if α > 0 , the hub nodes can use its degree advantage to collect more payoff; if α 0 , numerous non-hub nodes will obtain more payoff in a single round game. Simulation results show that the cooperation level has a non-trivial dependence on α . For the small enhancement factor r , the cooperator frequency can be promoted by both negative and positive α . For large r , there exists an optimal α that can obtain the highest cooperation level. Our results may sharpen the understanding of the emergence of cooperation induced by the unequal payoff allocation mechanism.

In this paper, traffic flow at a signal controlled T-shaped intersection with three input roads is investigated by using the cellular automata model. When each road is a double lane, the model only exists in three conflict points among three directions of flows. We introduce three-phase traffic signal and two types of signal controlling strategies, i.e. fixed signal phase order as well as adaptive signal phase order strategy, to control the traffic flow at the intersection. The phase diagram, the capacity and the average travel time of the system are investigated and compared under both strategies. The simulation results show that the traffic adaptive signal strategy is better than the fixed signal phase order strategy.

In traffic systems, a reasonable information feedback can improve road capacity. In this Letter, we study dynamics of traffic flow with real-time information. And the influence of a feedback strategy named Weighted Congestion Coefficient Feedback Strategy (WCCFS) is introduced, based on a two-route scenario in which dynamic information can be generated and displayed on the board to guide road users to make a choice. Our model incorporates the effects of adaptability into the cellular automaton models of traffic flow and simulation results adopting this optimal information feedback strategy have demonstrated high efficiency in controlling spatial distribution of traffic patterns compared with the other three information feedback strategies, i.e., vehicle number and flux.

A nonuniform payoff allocation mechanism is proposed for spatial public goods games where individuals are nodes on a scale-free network. Each individual is assigned a weight ki α, where ki is the degree of individual i and α is an adjustable parameter that controls the degree of diversity in individuals’ profits. During the evolution progress, the allocation of payoff on individual i is assumed to be proportional to its weight. Individuals synchronously update their strategies according to the stochastic rule with a fixed noise level. It is found that there exists an optimal value of α which yields the highest level of cooperation. Other pertinent quantities, including the payoff and the probability of finding a node playing as cooperator versus the degree, are also investigated computationally and analytically. Our results suggest that a suitable degree of diversity among individuals can promote the emergence of cooperation.

In this paper, we study the capacity of a highway with two on-ramps by using a cellular automata traffic flow model. We investigate how to improve the system capacity by assigning traffic flow to the two ramps. The system phase diagram is presented and different regions are classified. It is shown that in region I, in which both ramps are in free flow and the main road upstream of the ramps is in congestion, assigning a higher proportion of the demand to the upstream on-ramp could improve the overall flow, which is consistent with previous studies. This is explained through studying the spatiotemporal patterns and analytical investigations. In contrast, optimal assignment has not been observed in other regions. We point out that our result is robust and model independent under certain conditions.

In this paper, we study the dynamical behaviour of an epidemic on complex networks with population mobility. In our model, the number of people on each node is unrestricted as the nodes of the network are considered as cities, communities, and so on. Because people can travel between difierent cities, we study the efiect of a population’s mobility on the epidemic spreading. In view of the population’s mobility, we suppose that the susceptible individual can be infected by an infected individual in the same city or other connected cities. Simulations are presented to verify our analysis.

In traffic system, a reasonable information feedback can improve road capacity. In this paper, we investigate an asymmetrical two-route scenario in which dynamic information can be generated and displayed on the board to guide drivers. Two improved feedbacks (i.e. improved mean velocity feedback and improved congestion coefficient feedback) are introduced. Simulations show that the average cost is dependent on the vehicle arrival rate and there exists a critical the dynamic vehicles ratio corresponding to the maximum flux. We find that improved con-gestion coefficient can better enhance the system capacity than that of improved mean velocity feedback.

In this paper, we incorporate a limitation on the interaction range between neighboring vehicles into the cellular automaton model proposed by Gao and Jiang et al. [K. Gao, R. Jiang, S. X. Hu, B. H. Wang and Q. S. Wu, Phys. Rev. E 76 (2007) 026105], which was established within the framework of Kerner’s three-phase traffic theory and has been shown to be able to reproduce the three-phase traffic flow. This modification eliminates an unrealistic phenomenon found in the previous model, where the velocity-adaptation effect between neighboring vehicles can exist even if those vehicles are infinitely far away from each other. Therefore, in the improved model, we regulate that such interactions can only occur within a finite distance. For simplicity, we suppose a constant value to describe this distance in this paper. As a result, when compared to the previous model, the improved model mainly simulates the following results which are believed to be an improvement. (1) The improved model successfully reproduces the expected discontinuous transition from free flow to synchronized flow and the related “moving synchronized flow pattern”, which are both absent in the original model but have been observed in real traffic. (2) The improved model simulates the correlation functions, time headway distributions and optimal velocity functions which are all more consistent with the empirical data than the previous model and most of the other models published before. (3) Together with the previous two models considering the velocity-difference effect, this model finally accomplishes a significative process of developing traffic flow models from the traditional “fundamental diagram approach” to the three-phase traffic theory. This process should be helpful for us to understand the traffic dynamics and mechanics further and deeper.

In this paper, we propose a influence-based approach to investigate network-based recommendation systems. Different from the previous mass diffusion approach, we give a new expression of initial resource distribution and take into account the influence of resources associated with the receiver nodes. According to ranking score and two measures about the degree of personalization, we demonstrate that our method can outperform the previous methods greatly. It’s found that there exists an optimal initial resource distribution that leads to the best algorithmic accuracy and personalization strength. The optimal initial resource distribution indicates that we should increase the initial resource located on popular objects, rather than decrease them.

Ayurvedic oil-dripping treatment, Shirodhara, involves the use of medicated herbal sesame oils. In our previous reports, we found that Shirodhara with plain sesame oil induced anxiolysis and an altered state of consciousness (ASC) in healthy subjects. We studied the pharmaco-physio-psychologic effect of Shirodhara with medicated sesame oil including an essential oil from Lavendula angustifolia (lavender) in the present study. Sixteen (16) healthy females (38 +/- 8 years old) were assigned at random to three treatments applied by a robotic oil-dripping system: plain sesame oil (plain Shirodhara), medicated sesame oil with a 0.3 volume % of lavender essential oil (lavender Shirodhara), or the control supine position. Psychophysiologic parameters including the heart rate, skin temperature of the dorsum of hands and feet, as well as anxiety and ASC were monitored, and the rates of change of these items were calculated to assess the psychophysiologic changes brought about by Shirodhara. Lavender Shirodhara showed potent anxiolytic and ASC-inducing or promoting effects, and induced the largest increase in foot skin temperature. The correlation between anxiolysis and ASC, as well as the correlation between these psychologic effects and the elevated foot skin temperature were larger in the lavender Shirodhara than in the other two conditions. It was speculated that the psycho-physiologic effects of lavender Shirodhara would be brought about by three mechanisms: (1) the well-known relaxing action of essential oils from L. angustifolia mediated by olfactory nerves, (2) the pharmacologic action of substances absorbed through the skin or mucosa in the sesame oil or lavender essential oil, and (3) the physiologic effect of sesame oil dripped on the forehead induced by the somato-autonomic reflex through thermosensors or pressure sensors in the skin or hair follicles via the trigeminal cranial nerve. The complicated pharmaco-physio-psychologic action of Ayurvedic oil treatment may provide a useful model for future pharmaco-physio-psychotherapy.

In this paper, we numerically investigate the structural characteristics that affect the synchronizability of coupled identical oscillators on scale-free networks. By using the edge-exchange method, we can change the network structure with degree sequence fixed. An optimal algorithm, namely Tabu Search, is applied, respectively, to enhance and weaken the synchronizability. The numerical results indicate that the synchronizability is most sensitive to the maximal betweenness. By tracking the optimization process, most previous works suggest that the synchonizability can be enhanced by reducing assortative coefficient and clustering coefficient; however, interestingly, our numerical simulations show that the depression of synchronizability also corresponds to the reduction process of those two coefficients.

In this paper, we analytically study the probabilistic accelerating network [M.J. Gagen, J.S. Mattick, Phys. Rev. E 72 (2005) 016123] in its accelerating regimes by using mean field theory. In the growing network, the number of links added with each new node is a nonlinearly increasing function a N β ( t ) where N ( t ) is the number of nodes present at time t . It is found that the network appears to have a power-law degree distribution for large degree with tunable degree exponents (ranging from 3.0 to theoretically infinity) and the degree exponent γ depends only on the parameter β as γ = 1 + 2 1 − β . The analytical results are found to be in good agreement with those obtained by extensive numerical simulations.

The dynamics of information traffic over scale-free networks has been investigated systematically. A series of routing strategies of data packets have been proposed, including the local routing strategy, the next-nearest-neighbour routing strategy, and the mixed routing strategy based on local static and dynamic information. The capacity of the network can be quantified by the phase transition from free flow state to congestion state. The optimal parameter values of each model leading to the highest efficiency of scale-free networked traffic systems have been found. Moreover, we have found hysteretic loop in networked traffic systems with finite packets delivering ability. Such hysteretic loop indicates the existence of the bi-stable state in the traffic dynamics over scale-free networks.

The transition from a non-chaotic state to a chaotic state is an important issue in the study of coupled dynamical networks. In this paper, by using the theoretical analysis and numerical simulation, we study the dynamical behaviors of the NW small-world dynamical network consisting of nodes that are in non-chaotic states before they are coupled together. It is found that, for any given coupling strength and a sufficiently large number of nodes, the small-world dynamical network can be chaotic, even if the nearest-neighbor coupled network cannot be chaotic under the same condition. More interesting, the numerical results show that the measurement 1 R of the transition ability from non-chaos to chaos approximately obeys power-law forms as 1 R ∼ p - r 1 and 1 R ∼ N - r 2 . Furthermore, based on dissipative system criteria, we obtain the relationship between the network topology parameters and the coupling strength when the network is stable in the sense of Lyapunov (i. s. L.).

This paper presents a car-following model that considers the asymmetric characteristic of the velocity differences of the vehicles in a traffic stream. The problems of the prevalent general force (GF) model and the full velocity difference (FVD) model were solved. Furthermore, the optimal velocity (OV) model, the GF model, and the FVD model are proved to be the special cases of the proposed asymmetric full velocity difference (AFVD) model. The mathematical model is presented, followed by simulation analysis which demonstrates the properties of the AFVD model.

We propose a novel capacity model for complex networks against cascading failure. In this model, vertices with both higher loads and larger degrees should be paid more extra capacities, i.e. the allocation of extra capacity on vertex $i$ will be proportional to $ k_{i}^{\gamma} $, where $ k_{i}$ is the degree of vertex $i$ and $\gamma>0$ is a free parameter. We have applied this model on Barab\'asi-Albert network as well as two real transportation networks, and found that under the same amount of available resource, this model can achieve better network robustness than previous models., Comment: 4 pages, 4 figures

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

Additional to the basic Nagel–Schreckenberg model for single-lane traffic flow, we consider the effect of the velocity-difference between two successive vehicles on the randomization of the latter one. This modification improves the transit capacity of the model, which results in a much higher simulated flux. Moreover, in a circular road, this model simulates an abnormal hysteresis effect. The characteristic shape of hysteresis curves may shed some light on the distinguish of synchronized flow and jams.

The structural and dynamical properties, particularly the small-world effect and scale-free feature, of complex networks have attracted tremendous interest and attention in recent years. This article offers a brief review of one focal issue concerning the structural and dynamical behaviors of complex network synchronization. In the presentation, the notions of synchronization of dynamical systems on networks, stability of dynamical networks, and relationships between network structure and synchronizability, will be first introduced. Then, various technical methods for enhancing the network synchronizability will be discussed, which are roughly divided into two classes: Structural Modification and Coupling-Pattern Regulation, where the former includes three typical methods—dividing hub nodes, shortening average distances, and deleting overload edges, while the latter mainly is a method of strengthening the hub-nodes’ influence on the network.

We investigate the dynamics of network minority games on Kauffman's NK networks (Kauffman nets) and growing directed networks (GDNets). We show that the dynamics and the associated phase structure of the game depend crucially on the structure of the underlying network. The dynamics on GDNets is very stable for all values of the connection number K, in contrast to the dynamics on Kauffman's NK networks, which becomes chaotic when K > Kc= 2. For Kauffman nets with K > 3, the evolutionary scheme has no effect on the dynamics (it remains chaotic) and the performance of the MG resembles that of a random choice game (RCG).

In this Letter, we propose a growing network model that can generate scale-free networks with a tunable community strength. The community strength, C, is directly measured by the ratio of the number of external edges to that of the internal ones; a smaller C corresponds to a stronger community structure. By using the Kuramoto model, we investigated the phase synchronization on this network and found an abnormal region ( C ⩽ 0.002 ), in which the network has even worse synchronizability than the unconnected case ( C = 0 ). On the other hand, the community effect will vanish when C exceeds 0.1. Between these two extreme regions, a stronger community structure will hinder global synchronization.