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To understand the relations between developers and software, we study a collaborative coding platform from the perspective of networks, including follower networks, dependence networks and developer-project bipartite networks. Through the analyzing of degree distribution, PageRank and degree-dependent nearest neighbors’ centrality, we find that the degree distributions of all networks have a power-law form except the out-degree distributions of dependence networks. The nearest neighbors’ centrality is negatively correlated with degree for developers but fluctuates around the average for projects. In order to measure the diversity of profession levels of interests, a new index called dependence centrality similarity is proposed and the correlation between dependence centrality similarity and degree is investigated. The result shows an obvious negative correlations between dependence centrality similarity and degree.

Guided by a price-volume probability wave differential equation in a new mathematical method, we study intraday market dynamic equilibrium in stock market. We select intraday cumulative trading volume distribution over a price range as individual mental representation and determine a price equilibrium point by the maximum volume utility price. We propose the hypothesis that a stock price can deviate away from the equilibrium point in momentum and restore to it in reversal, and the volume distribution embodies market dynamic equilibrium. Then, we examine it by a set of explicit price dynamic equilibrium models with trading volume weights from the differential equation against a large number of the price-volume distribution using tick-by-tick high frequency data in Chinese stock market in 2019. It holds true. We can infer that the theory is applied for a broader scope because it embraces core mathematical components in expected utility theory, prospect theory, and reflexivity theory.

In this paper, we utilize Spearman rank correlation coefficient to measure mixing patterns in complex networks. Compared with the widely used Pearson coefficient, Spearman coefficient is rank-based, nonparametric, and size-independent. Thus it is more effective to assess linking patterns of diverse networks, especially for large-size networks. We demonstrate this point by testing a variety of empirical and artificial networks. Moreover, we show that normalized Spearman ranks of stubs are subject to an interesting linear rule where the correlation coefficient is just the Spearman coefficient. This compelling linear relationship allows us to directly produce networks with any prescribed Spearman coefficient. Our method apparently has an edge over the well known uncorrelated configuration model.

A method based on the breadth-first search tree is proposed in this paper to characterize the hierarchical structure of network. In this method, a similarity coefficient is defined to quantitatively distinguish networks, and quantitatively measure the topology stability of the network generated by a model. The applications of the method are discussed in ER random network, WS small-world network and BA scale-free network. The method will be helpful for deeply describing network topology and provide a starting point for researching the topology similarity and isomorphism of networks.

In this paper, we study how special patterns affect certain dynamic process on networks. The process we analyze is an iteration to generate a doubly-stochastic matrix consistent to the adjacent matrix of a network and the patterns can be described as h non-interconnected vertices only connect other g vertices ( h > g ) . From the perspective of network structure, we prove that the necessary and sufficient condition when the iteration converges is that these patterns do not exist in the network. For BA networks, there is a phase transition. The diverge–converge transition point is that the average degree is about 8, which is theoretically proved. The existence of these patterns depends on two factors: first, higher moments of degree distribution of the network; second, the probability that vertices with degree 1 exist in the network. Simulation results also support our theory.

For past decades, the main attention of the evolutionary games has been focused on cooperation mechanism with the assumption that the strategy information of all players are known. However, it is difficult for observers to obtain the global information of players' strategies in the real world, and some players even hide their strategy information to confuse their opponents. Here we try to solve the problem to predicate the hidden strategies with sparse historical behavior data in the evolutionary games. To quantify the similarity of strategies among the players in our method, the Euclidean distance of players is defined from the strategies of the players in the few past rounds. Then, the hidden strategy of a player will be determined from the tendency that players with minimum Euclidean distance will adopt similar strategies. The method has good performance on determining hidden strategy of human beings in both the prisoner's dilemma game and the public goods game where strategies of twenty five percent players are hidden, and the success rate to determine hidden strategy reaches up to 0.9. It is also found that the success rate to determine hidden strategy depends on both length of historical behavior data and tempting payoff b (the prisoner's dilemma game) or multiple factor r (the public goods game).

It has been proved that the degree correlation can affect the structural controllability of directed networks. Here, we explore the effect of interconnections’ correlation on the exact controllability of multiplex networks. We find that the minimal number of driver nodes decreases with correlation for lower density of interconnections. However, the controllability of networks with higher density of interconnections shows the contrary tendency. For different interconnections’ correlations, controllability of multiplex networks depicts transition with the density of interconnections. For lower interconnections density, the networks with disassortative coupling patterns are harder to control. Whereas, for higher interconnections density, the networks with assortative coupling patterns are harder to control.

We empirically study the activity pattern of individual blog-posting and observe the interevent time distributions decay as power-laws at both individual and population level. As different from previous studies, we find significant short-term memory in it. Moreover, the memory coefficient first decays in a power law and then turns to an exponential form. Our findings produce evidence for the strong short-term memory in human dynamics and challenge previous models. Accordingly, we propose a simple model based on temporal preference, which can well reproduce both the heavy-tailed nature and the strong memory effects. This work helps in understanding the temporal regularities of online human behaviors.

In real networks, the dependency between nodes is ubiquitous; however, the dependency is not always complete and homogeneous. In this paper, we propose a percolation model with weak and heterogeneous dependency; i.e., dependency strengths could be different between different nodes. We find that the heterogeneous dependency strength will make the system more robust, and for various distributions of dependency strengths both continuous and discontinuous percolation transitions can be found. For Erd\H{o}s-R\'{e}nyi networks, we prove that the crossing point of the continuous and discontinuous percolation transitions is dependent on the first five moments of the dependency strength distribution. This indicates that the discontinuous percolation transition on networks with dependency is determined not only by the dependency strength but also by its distribution. Furthermore, in the area of the continuous percolation transition, we also find that the critical point depends on the first and second moments of the dependency strength distribution. To validate the theoretical analysis, cases with two different dependency strengths and Gaussian distribution of dependency strengths are presented as examples., Comment: 8 pages, 8 figures

In this paper, we have captured an underlying mechanism of emergence of collective panic in pedestrian evacuations by using a modification of the lattice-gas model. We classify the motion of pedestrians into two modes according to their moods. One is gentle (mode I), the other is flustered (mode II). First, to research the cause for crowd, we fix the motion modes of pedestrians and increase the proportion of pedestrians with motion mode II (ρII). The simulation results show that the pedestrians with motion mode II are lack of evacuation efficiency and cause more casualties. Further, we use the SIS (susceptible-infective-susceptible) model to describe the spreading of the panic mood. The system can be in the high-mix state when the infection probability λ is greater than a fuzzy threshold. In addition, the distances S from wounded people to the exit are researched, the number of wounded people gets maximum at the internal S = 5 ∼ 10, which is independent of ρII and λ. This research can help us to understand and prevent the emergence of collective panic and reduce wounds in the real evacuation.

Information feedback strategy, serving as the critical part of intelligent traffic systems, has been treated with growing emphasis. In recent years, a variety of feedback strategies have been proposed. Despite the fact that these strategies have been proved to enhance the traffic efficiency, we find that the road capacity has not been saturated and there is still plenty of room for improvement. Based on the analytic approximations, we found the reason why corresponding angle feedback strategy is superior to weighted congestion coefficient feedback strategy. Given that the sharp decay of the weighted coefficient is the key point, we proposed an efficient feedback strategy called the exponential function feedback strategy (EFFS). We applied it to both the symmetrical two-route model with two exits and that with a single exit. The simulation results indicate that, compared with other strategies, EFFS has decided numerical advantages in average flow, a physical quantity used for depicting the road capacity. Even more importantly, EFFS stands out for its convenient application as well as its fitness for modeling the rugged roads.

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.

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 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.

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.

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 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 .

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, 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.

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 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 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 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

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).

By means of the diffusion entropy approach, we detect the scale-invariance characteristics embedded in the 4737 human promoter sequences. The exponent for the scale-invariance is in a wide range of $[ {0.3,0.9} ]$, which centered at $\delta_c = 0.66$. The distribution of the exponent can be separated into left and right branches with respect to the maximum. The left and right branches are asymmetric and can be fitted exactly with Gaussian form with different widths, respectively., Comment: 5 pages, 3 figures, To appear in Journal of Theoretical Biology

In this paper, we propose an alternative model for collaboration networks based on nonlinear preferential attachment. Depending on a single free parameter "preferential exponent", this model interpolates between networks with a scale-free and an exponential degree distribution. The degree distribution in the present networks can be roughly classified into four patterns, all of which are observed in empirical data. And this model exhibits small-world effect, which means the corresponding networks are of very short average distance and highly large clustering coefficient. More interesting, we find a peak distribution of act-size from empirical data which has not been emphasized before. Our model can produce the peak act-size distribution naturally that agrees with the empirical data well.

In this paper, firstly, we propose a complex dynamical network model, which is always uniformly asymptotically stable about its equilibrium. Then, we give theoretical analysis of its uniform asymptotical stability by using Lyapunov stability theory. Finally, we show a numerical example to verify our theoretical result.

As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two $k$-cliques means that they share at least $l1$ makes a step-function-like discontinuous phase transition in the thermodynamic limit and a continuous phase transition for $l=1$. More interesting, our analysis shows that at the critical point, the order parameter $\phi_c$ for $l>1$ is neither $0$ nor $1$, but a constant depending on $k$ and $l$. All these theoretical findings are in agreement with the simulation results, which give theoretical support and clarification for previous simulation studies of clique percolation., Comment: 6 pages, 5 figures

The self-controlling feedback control method requires an external periodic oscillator with special design, which is technically challenging. This paper proposes a chaos control method based on time series non-uniform rational B-splines (SNURBS for short) signal feedback. It first builds the chaos phase diagram or chaotic attractor with the sampled chaotic time series and any target orbit can then be explicitly chosen according to the actual demand. Second, we use the discrete timing sequence selected from the specific target orbit to build the corresponding external SNURBS chaos periodic signal, whose difference from the system current output is used as the feedback control signal. Finally, by properly adjusting the feedback weight, we can quickly lead the system to an expected status. We demonstrate both the effectiveness and efficiency of our method by applying it to two classic chaotic systems, i.e., the Van der Pol oscillator and the Lorenz chaotic system. Further, our experimental results show that compared with delayed feedback control, our method takes less time to obtain the target point or periodic orbit (from the starting point) and that its parameters can be fine-tuned more easily.

Controlling complex network is an essential problem in network science and engineering. Recent advances indicate that the controllability of complex network is dependent on the network's topology. Liu and Barabási, et.al speculated that the degree distribution was one of the most important factors affecting controllability for arbitrary complex directed network with random link weights. In this paper, we analysed the effect of degree distribution to the controllability for the deterministic networks with unweighted and undirected. We introduce a class of deterministic networks with identical degree sequence, called (x,y)-flower. We analysed controllability of the two deterministic networks ((1, 3)-flower and (2, 2)-flower) by exact controllability theory in detail and give accurate results of the minimum number of driver nodes for the two networks. In simulation, we compare the controllability of (x,y)-flower networks. Our results show that the family of (x,y)-flower networks have the same degree sequence, but their controllability is totally different. So the degree distribution itself is not sufficient to characterize the controllability of deterministic networks with unweighted and undirected.

How to identify the influential spreaders in social networks is crucial for accelerating/hindering information diffusion, increasing product exposure, controlling diseases and rumors, and so on. In this paper, by viewing the k-shell value of each node as its mass and the shortest path distance between two nodes as their distance, then inspired by the idea of the gravity formula, we propose a gravity centrality index to identify the influential spreaders in complex networks. The comparison between the gravity centrality index and some well-known centralities, such as degree centrality, betweenness centrality, closeness centrality, and k-shell centrality, and so forth, indicates that our method can effectively identify the influential spreaders in real networks as well as synthetic networks. We also use the classical Susceptible-Infected-Recovered (SIR) epidemic model to verify the good performance of our method., Comment: 4 tables and 4 figures, accepted by Physica A

Inspired by Pythagoras's belief that numbers represent the reality, we study the topological properties of networks of composite numbers, in which the vertices represent the numbers and two vertices are connected if and only if there exists a divisibility relation between them. The network has a fairly large clustering coefficient C ≈ 0.34 , which is insensitive to the size of the network. The average distance between two nodes is shown to have an upper bound that is independent of the size of the network, in contrast to the behavior in small-world and ultra-small-world networks. The out-degree distribution is shown to follow a power-law behavior of the form k - 2 . In addition, these networks possess hierarchical structure as C ( k ) ∼ k - 1 in accord with the observations of many real-life networks.

Using homogenous partition of coarse graining process, the time series of Hang Seng Index (HSI) in Hong Kong stock market is transformed into discrete symbolic sequences S={S1S2S3...}, Si ∈ (R, r, d, D). Weighted networks of stock market are constructed by vertices that are 16 2-symbol strings (i.e. 16 patterns of HSI variations), and encode stock market relevant information about interconnections and interactions between fluctuation patterns of HSI in networks topology. By means of the measurements of betweenness centrality (BC) in networks, we have at least obtained 3 highest betweenneess centrality uniform vertices in 2 order of magnitude of time subinterval scale, i.e. 18.7% vertices undertake 71.9% betweenness centrality of networks, showing statistical stability. These properties cannot be found in random networks; here vertices almost have identical betweenness centrality. By comparison to random networks, we conclude that Hong Kong stock market, rather than a random system, is statistically stable.

A simple model is proposed to mimic and study the evolution of interpersonal relationships in a student class. The small social group is simply assumed as an undirected and weighted graph, in which students are represented by vertices, and the depth of favor or disfavor between them are denoted by the corresponding edge weight. In our model, we find that the first impression between people has a crucial influence on the final status of student relations (i.e., the final distribution of edge weights). The system displays a phase transition in the final hostility proportion depending on the initial amity possibility. We can further define the strength of vertices to describe the individual popularity, which exhibits nonlinear evolution. Meanwhile, various nonrandom perturbations to the initial system have been investigated, and simulation results are in accord with common real-life observations.

In this letter, we investigate the detailed epidemic spreading process in scale-free networks with links' weights that denote familiarity between two individuals and find that spreading velocity reaches a peak quickly then decays in a power-law form. Numerical study exhibits that the nodes with larger strength is preferential to be infected, but the hierarchical dynamics are not clearly found, which is different from the well-known result in unweighed network case. In addition, also by numerical study, we demonstrate that larger dispersion of weight of networks results in slower spreading, which indicates that epidemic spreads more quickly on unweighted scale-free networks than on weighted scale-free networks with the same condition., 4 pages, 5 figures. Chin. Phys. Lett in Press 2005

How to detect unstable periodic orbits (UPOs) which reside on the chaotic attractors is an important problem in diverse scientific fields. In this paper, we present an efficient algorithm for computing UPOs. It can be applied to any finite dimensional chaotic systems including hyperchaotic systems. We also discuss numerically the converging regions of the algorithm here. The chaotic Henon map is taken as numerical example in the text.

An artificial stock market is established with the modeling method and ideas of cellular automata. Cells are used to represent stockholders, who have the capability of self-teaching and are affected by the investing history of the neighboring ones. The neighborhood relationship among the stockholders is the expanded Von Neumann relationship, and the interaction among them is realized through selection operator and crossover operator. Experiment shows that the large events are frequent in the fluctuations of the stock price generated by the artificial stock market when compared with a normal process and the price returns distribution is a Levy distribution in the central part followed by an approximately exponential truncation., 5 pages, 4 figures, to be published in

The method of controlling chaos by occasional nonlinear time-delayed feedback is proposed. Through the numerical analysis of bifurcation diagram and Lyapunov exponent, we found that the systematic chaos can be controlled effectively by the nonlinear time-delayed feedback as the form of u(xn,xn-k)=cxnxn-k. Under the proper feedback coefficient c, time-delayed coefficient k and occasional feedback period N, the system could be controlled from chaos to the steady periodic orbit, and also the steady period is the integral multiple of the occasional feedback period N.

Based on the adiabatic theory for the evolutionary minority game (EMG) that we proposed earlier[1], we perform a detail analysis of the EMG limited to three groups of agents. We derive a formula for the critical point of the transition from segregation (into opposing groups) to clustering (towards cautious behaviors). Particular to the three-group EMG, the strategy switching in the "extreme" group does not occur at every losing step and is strongly intermittent. This leads to an correction to the critical value of the number of agents at the transition, $N_c$. Our expression for $N_c$ is in agreement with the results obtained from our numerical simulations., 4 pages and 2 figures

Some parameters are introduced to evaluate the completeness of a partial multifractal spectrum with the shape of a bell or a hook, calculated using a statistical method due to a finite range of moment q. From the results of two kinds of Cantor sets, p/0/1-p and p/1-2p/p, and some examples of random fractals, it shows that the more homogeneous the probability distribution of the quantity studied is, the larger the range of q in the partial multifractal spectrum with the same evaluation parameters.

The daily Hang Seng index in the Hong Kong stock market has been analyzed in this paper. Two kinds of sign sequences as given conditions have been used to predict the future price movements. One is the parameter of multifractal spectrum Δ f based on the indexes recorded in every minute, and the other is the variation of the close index Δ i . Results show that correlation between large fluctuations of the close price and the condition in these two methods is strong and some sign sequences of the parameter Δ f can be used to predict the probability of the near future price movements.

In recent years, synchronization of chaotic systems has aroused much interest due to its potential application to secure communications. However, it is found by Perez and Cerdeira that an intruder, without the knowledge of the parameters of the system or even of the nonlinear system itself, may extract the messages from the carrier signal by producing a return map where the dynamics is attracted to an almost 1D set. To eliminate the weakness, in this letter, a simple but efficient method for synchronizing chaotic systems by modulating the transmitted signal with an appropriately choosing scalar signal is proposed. It turns out that this modulating strategy not only preserves all appropriate information required for synchronizing chaotic systems but also destroys the possibility of the phase space reconstruction of the sender dynamics such as a return map.

In this paper, we shall present our studies of a generalized evolutionary minority game model in which the agents are divided into several groups. The performance of the individual agent is averaged in each group. We find that there are three different effects in this generalized model, i.e. (1) group averaging effect, (2) left-right asymmetric effect, and (3) self-interaction effect. The former two effects favor the cautious agents, while the last one favors the extreme agents. In most cases, both the analytic results and the numerical simulations demonstrate that the group averaging effect is dominantly important and therefore the performance of the cautious agents is better than that of the extreme agents. However, when the number of groups is sufficiently large, the generalized model can be somehow reduced to the conventional evolutionary minority game model. As the parameters vary in the generalized model, the importance of the above three effects is exchangeable and different types of population distribution emerge.

We propose a method for controlling chaos and hyper-chaos by applying continuous proportional feedback to the system variables and their derivatives. The method has been applied successfully in six-order coupled Chua's hyper-chaotic circuit system. The theoretical analysis and numerical simulation results show that unstable fixed points embedded in hyper-chaotic attractors can be stabilized and Hopf bifurcation can be observed for the controlled system.

In this paper, controlling chaos in the chaotic n-scroll Chua's circuit is studied. The approach taken is to use feedback of a single state variable in a simple PD (proportional and differential) format. First, the unstable fixed points in the n-scroll Chua's circuit are classified into two different types according to the characteristics of the eigenvalues of the linearized system matrix at the fixed points. Then, the controllability of these two-types of fixed points is studied. Theoretical analysis shows that the first type of unstable fixed points can be stabilized, at which Hopf bifurcation can also be generated. Control results of the n-scroll Chua's circuit are then demonstrated. Both theoretical analysis and numerical simulation results show that the proposed chaos control method is indeed effective.

We propose and study a modified version of the evolutionary minority game consisting of a competing population. Agents in the population are repeatedly competing to be in a minority and they have a common strategy. Each agent has a parameter p characterizing the probability that she is following the prediction of the common strategy. Agents are lined up in a one-dimensional chain with periodic boundary condition. Imitation is allowed among nearest neighboring agents. Numerical results show that the agents evolve into a state in which they self-segregate into opposite groups characterized by extreme behavior and imitation leads to considerable enhancement in the overall performance of the population.

We study the controllability of networks in the process of cascading failures under two different attacking strategies, random and intentional attack, respectively. For the highest-load edge attack, it is found that the controllability of Erdős-Rényi network, that with moderate average degree, is less robust, whereas the Scale-free network with moderate power-law exponent shows strong robustness of controllability under the same attack strategy. The vulnerability of controllability under random and intentional attacks behave differently with the increasing of removal fraction, especially, we find that the robustness of control has important role in cascades for large removal fraction. The simulation results show that for Scale-free networks with various power-law exponents, the network has larger scale of cascades do not mean that there will be more increments of driver nodes. Meanwhile, the number of driver nodes in cascading failures is also related to the edges amount in strongly connected components.