Showing papers in "Physica A-statistical Mechanics and Its Applications in 2011"

Link prediction in complex networks: A survey

Abstract: Link prediction in complex networks has attracted increasing attention from both physical and computer science communities. The algorithms can be used to extract missing information, identify spurious interactions, evaluate network evolving mechanisms, and so on. This article summaries recent progress about link prediction algorithms, emphasizing on the contributions from physical perspectives and approaches, such as the random-walk-based methods and the maximum likelihood methods. We also introduce three typical applications: reconstruction of networks, evaluation of network evolving mechanism and classification of partially labeled networks. Finally, we introduce some applications and outline future challenges of link prediction algorithms.

DCCA cross-correlation coefficient: Quantifying level of cross-correlation

Abstract: In this paper, a new coefficient is proposed with the objective of quantifying the level of cross-correlation between nonstationary time series. This cross-correlation coefficient is defined in terms of the DFA method and the DCCA method. The implementation of this cross-correlation coefficient will be illustrated with selected time series.

Rumor spreading model with consideration of forgetting mechanism: A case of online blogging LiveJournal

Abstract: Rumor is an important form of social interaction, and its spreading has a significant impact on people’s lives. In the age of Web, people are using electronic media more frequently than ever before, and blog has become one of the main online social interactions. Therefore, it is essential to learn the evolution mechanism of rumor spreading on homogeneous network in consideration of the forgetting mechanism of spreaders. Here we study a rumor spreading model on an online social blogging platform called LiveJournal. In comparison with the Susceptible–Infected–Removed (SIR) model, we provide a more detailed and realistic description of rumor spreading process with combination of forgetting mechanism and the SIR model of epidemics. A mathematical model has been presented and numerical solutions of the model were used to analyze the impact factors of rumor spreading, such as the average degree, forgetting rate and stifling rate. Our results show that there exist a threshold of the average degree of LiveJournal and above which the influence of rumor reaches saturation. Forgetting mechanism and stifling rate exert great influence on rumor spreading on online social network. The analysis results can guide people’s behaviors in view of the theoretical and practical aspects.

Identifying the community structure of the international-trade multi-network

Abstract: We study the community structure of the multi-network of commodity-specific trade relations among world countries over the 1992–2003 period. We compare structures across commodities and time by means of the normalized mutual information index (NMI). We also compare them with exogenous community structures induced by geography and regional trade agreements. We find that commodity-specific community structures are very heterogeneous and much more fragmented than that characterizing the aggregate ITN. This shows that the aggregate properties of the ITN may result (and be very different) from the aggregation of very diverse commodity-specific layers of the multi-network. We also show that commodity-specific community structures, especially those related to the chemical sector, are becoming more and more similar to the aggregate one. Finally, our findings suggest that geography-induced partitions of our set of countries are much more correlated with observed community structures than partitions induced by regional-trade agreements. This result strengthens previous findings from the empirical literature on trade.

Network analysis of a financial market based on genuine correlation and threshold method

Abstract: A financial market is an example of an adaptive complex network consisting of many interacting units. This network reflects market’s behavior. In this paper, we use Random Matrix Theory (RMT) notion for specifying the largest eigenvector of correlation matrix as the market mode of stock network. For a better risk management, we clean the correlation matrix by removing the market mode from data and then construct this matrix based on the residuals. We show that this technique has an important effect on correlation coefficient distribution by applying it for Dow Jones Industrial Average (DJIA). To study the topological structure of a network we apply the removing market mode technique and the threshold method to Tehran Stock Exchange (TSE) as an example. We show that this network follows a power-law model in certain intervals. We also show the behavior of clustering coefficients and component numbers of this network for different thresholds. These outputs are useful for both theoretical and practical purposes such as asset allocation and risk management.

Negative emotions boost user activity at BBC forum

Abstract: We present an empirical study of user activity in online BBC discussion forums, measured by the number of posts written by individual debaters and the average sentiment of these posts. Nearly 2.5 million posts from over 18 thousand users were investigated. Scale-free distributions were observed for activity in individual discussion threads as well as for overall activity. The number of unique users in a thread normalized by the thread length decays with thread length, suggesting that thread life is sustained by mutual discussions rather than by independent comments. Automatic sentiment analysis shows that most posts contain negative emotions and the most active users in individual threads express predominantly negative sentiments. It follows that the average emotion of longer threads is more negative and that threads can be sustained by negative comments. An agent-based computer simulation model has been used to reproduce several essential characteristics of the analyzed system. The model stresses the role of discussions between users, especially emotionally laden quarrels between supporters of opposite opinions, and represents many observed statistics of the forum.

Multigroup SIR epidemic model with stochastic perturbation

Abstract: In this paper, we discuss a multigroup SIR model with stochastic perturbation. We deduce the globally asymptotic stability of the disease-free equilibrium when R 0 ≤ 1 , which means the disease will die out. On the other hand, when R 0 > 1 , we derive the disease will prevail, which is measured through the difference between the solution and the endemic equilibrium of the deterministic model in time average. Furthermore, we prove the system is persistent in the mean which also reflects the disease will prevail. The key to our analysis is choosing appropriate Lyapunov functions. Finally, we illustrate the dynamic behavior of the model with n = 2 and their approximations via a range of numerical experiments.

Networked analysis of the Shanghai subway network, in China

Abstract: Recently, cities have become larger and larger, and more and more people are living in large cities. This phenomenon has caused serious traffic congestion which is very detrimental to the development of large cities. In this context, the subway has become the most effective solution for relieving traffic congestion and subways have been constructed in many cities, so the reliability and robustness of subways should be guaranteed. In this paper, Shanghai subway network, in China, will be analyzed and investigated; the topological characteristics and functional properties can be studied in order to assess the reliability and robustness. The topological characteristics can be measured using several parameters; meanwhile the fraction of removed nodes of Shanghai subway network is discussed and compared against that for a random network, and the critical threshold of this fraction is obtained. Two novel parameters called the functionality loss and connectivity of subway lines are proposed for measuring the transport functionality and the connectivity of subway lines. Subway lines 4 and 7 are selected as examples for evaluating the connectivity of lines subjected to different attack protocols. This study indicates that the subway network is robust against random attacks but fragile for malicious attacks, and the highest betweenness node-based attacks can cause the most serious damage to subway networks among the different attack protocols.

First passage time statistics of Brownian motion with purely time dependent drift and diffusion

Abstract: Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by time-dependent drift and diffusion coefficients. Modeling such systems requires solving the associated Fokker-Planck equation subject to an absorbing barrier. Transitional probabilities are derived via the method of images, whose applicability to time dependent problems is shown to be limited to state-independent drift and diffusion coefficients that only depend on time and are proportional to each other. First passage time statistics, such as the survival probabilities and first passage time densities are obtained analytically. The analysis includes the study of different functional forms of the time dependent drift and diffusion, including power-law time dependence and different periodic drivers. As a case study of these theoretical results, a stochastic model of water resources availability in snowmelt dominated regions is presented, where both temperature effects and snow-precipitation input are incorporated.

Room evacuation in the presence of an obstacle

Abstract: The investigation of human behaviour while trying to escape from a room under panic is an important issue in complex systems research. Several authors have called attention to the fact that placing an obstacle near the exit improves the evacuation time of the room (Helbing et al. (2000, 2005) [2] , [8] , Hughes (2003) [6] , Johansson and Helbing (2005) [16] , Piccoli and Tosin (2009) [5] ). We studied this effect in the context of the “social force model” (Helbing et al. (2000) [2] ). We show that placing an obstacle does not guarantee, by itself, better chances of survival for all pedestrians. The way they choose to avoid the obstacle is critical for their own performance. We found not only that the faster they try to escape, the slower they get out (“faster is slower” effect), but also, the short cut they might take in order to get to the exit will probably do no better (“clever is not always better” effect).

Analysis of the efficiency and multifractality of gold markets based on multifractal detrended fluctuation analysis

Abstract: In this paper, we investigate the efficiency and multifractality of a gold market based on multifractal detrended fluctuation analysis. Our evidence shows that the gold return series are multifractal both for time scales smaller than a month and for time scales larger than a month. For time scales smaller than a month, the main contribution of multifractality is fat-tail distribution. For time scales larger than a month, both long-range correlations and fat-tail distribution play important roles in the contribution of multifractality. Using the method of rolling windows, we find that the gold market became more and more efficient over time, especially after 2001. The abnormal points of scaling exponents can also be related to some occasional events. By defining a new inefficiency measure related to the multifractality, we find that the gold market is more efficient during the upward periods than during the downward periods.

A new approach to quantify power-law cross-correlation and its application to commodity markets

Abstract: We proposed a new method: Detrended Moving-average Cross-correlation Analysis (DMCA) to detect the power-law cross-correlation between two correlated non-stationary time series by combining Detrended Cross-Correlation Analysis (DCCA) and Detrended Moving Average (DMA). In order to compare the performance of DMCA and DCCA in the detection of cross-correlation, and to estimate the influence of periodic trend, we generate two cross-correlated time series x ( i ) and y ( i ) by a periodic two-component fractionally autoregressive integrated moving average (ARFIMA) process. Then we apply both methods to quantify the cross-correlations of the generated series, whose theoretical values are already known to us. By comparing the results we obtained, we find that the performance of this new approach is comparable to DCCA with less calculating amounts; our method can also reduce the impact of trends; furthermore, DMCA (for background and forward moving average case) outperforms DCCA in more accurate estimation when the analyzed times series are short in length. To provide an example, we also apply this new method to the time series of the real-world data from Brent and WTI crude oil spot markets, to investigate the complex cross-market correlation between these commodity markets. In all, our method is another practical choice to detect the cross-correlation between two short period non-stationary time series, and has potential application to real world problems.

Detrended fluctuation analysis on spot and futures markets of West Texas Intermediate crude oil

Abstract: In this paper, we study the auto-correlations and cross-correlations of West Texas Intermediate (WTI) crude oil spot and futures return series employing detrended fluctuation analysis (DFA) and detrended cross-correlation analysis (DCCA). Scaling analysis shows that, for time scales smaller than a month, the auto-correlations and cross-correlations are persistent. For time scales larger than a month but smaller than a year, the correlations are anti-persistent, while, for time scales larger than a year, the series are neither auto-correlated nor cross-correlated, indicating the efficient operation of the crude oil markets. Moreover, for small time scales, the degree of short-term cross-correlations is higher than that of auto-correlations. Using the multifractal extension of DFA and DCCA, we find that, for small time scales, the correlations are strongly multifractal, while, for large time scales, the correlations are nearly monofractal. Analyzing the multifractality of shuffled and surrogated series, we find that both long-range correlations and fat-tail distributions make important contributions to the multifractality. Our results have important implications for market efficiency and asset pricing models.

Nonlinear bivariate dependency of price–volume relationships in agricultural commodity futures markets: A perspective from Multifractal Detrended Cross-Correlation Analysis

Abstract: Nonlinear dependency between characteristic financial and commodity market quantities (variables) is crucially important, especially between trading volume and market price. Studies on nonlinear dependency between price and volume can provide practical insights into market trading characteristics, as well as the theoretical understanding of market dynamics. Actually, nonlinear dependency and its underlying dynamical mechanisms between price and volume can help researchers and technical analysts in understanding the market dynamics by integrating the market variables, instead of investigating them in the current literature. Therefore, for investigating nonlinear dependency of price–volume relationships in agricultural commodity futures markets in China and the US, we perform a new statistical test to detect cross-correlations and apply a new methodology called Multifractal Detrended Cross-Correlation Analysis (MF-DCCA), which is an efficient algorithm to analyze two spatially or temporally correlated time series. We discuss theoretically the relationship between the bivariate cross-correlation exponent and the generalized Hurst exponents for time series of respective variables. We also perform an empirical study and find that there exists a power-law cross-correlation between them, and that multifractal features are significant in all the analyzed agricultural commodity futures markets.

Consensus analysis and design for high-order linear swarm systems with time-varying delays

Abstract: Consensus analysis and design problems for high-order linear time-invariant swarm systems with time-varying delays are dealt with. First, a consensus subspace and a complement consensus subspace are introduced. By the state projection onto the two subspaces, consensus problems are converted into simultaneous stabilization problems of multiple time-delayed subsystems with low dimensions, and a method to analyze and design the consensus function is given. Then, sufficient conditions for consensus and consensualization are presented, which include only four linear matrix inequality constraints. Finally, theoretical results are applied to deal with cooperative control problems of multi-agent supporting systems.

An electrical betweenness approach for vulnerability assessment of power grids considering the capacity of generators and load

Abstract: Most existing research on the vulnerability of power grids based on complex networks ignores the electrical characteristics and the capacity of generators and load. In this paper, the electrical betweenness is defined by considering the maximal demand of load and the capacity of generators in power grids. The loss of load, which reflects the ability of power grids to provide sufficient power to customers, is introduced to measure the vulnerability together with the size of the largest cluster. The simulation results of the IEEE-118 bus system and the Central China Power Grid show that the cumulative distributions of node electrical betweenness follow a power-law and that the nodes with high electrical betweenness play critical roles in both topological structure and power transmission of power grids. The results prove that the model proposed in this paper is effective for analyzing the vulnerability of power grids.

Evacuation dynamics with fire spreading based on cellular automaton

Abstract: This paper investigates the dynamics of pedestrian evacuation with the influence of the fire spreading. An extended floor field model is proposed. In the new model, the effect of fire on the evacuation is considered by introducing the fire floor field. Thus, the floor field intensity is weighted by static, dynamic and fire floor fields. Numerical simulations are carried out to study the dynamics in the process of the evacuation. The influence of the parameters–weight of fire floor field, fire spread rate–on the evacuation efficiency is analyzed in detail. The simulation results show that the number of pedestrians evacuated out of the room is highly related to both the original location of the fire and the configuration of the room. Those results can bring some guidance to design the evacuation strategy in panic situation.

A characterization of horizontal visibility graphs and combinatorics on words

Abstract: A Horizontal Visibility Graph (HVG) is defined in association with an ordered set of non-negative reals. HVGs realize a methodology in the analysis of time series, their degree distribution being a good discriminator between randomness and chaos Luque et al. [B. Luque, L. Lacasa, F. Ballesteros, J. Luque, Horizontal visibility graphs: exact results for random time series, Phys. Rev. E 80 (2009), 046103]. We prove that a graph is an HVG if and only if it is outerplanar and has a Hamilton path. Therefore, an HVG is a noncrossing graph, as defined in algebraic combinatorics Flajolet and Noy [P. Flajolet, M. Noy, Analytic combinatorics of noncrossing configurations, Discrete Math., 204 (1999) 203–229]. Our characterization of HVGs implies a linear time recognition algorithm. Treating ordered sets as words, we characterize subfamilies of HVGs highlighting various connections with combinatorial statistics and introducing the notion of a visible pair. With this technique, we determine asymptotically the average number of edges of HVGs.

Currency crises and the evolution of foreign exchange market: Evidence from minimum spanning tree

Abstract: We examined the time series properties of the foreign exchange market for 1990–2008 in relation to the history of the currency crises using the minimum spanning tree (MST) approach and made several meaningful observations about the MST of currencies. First, around currency crises, the mean correlation coefficient between currencies decreased whereas the normalized tree length increased. The mean correlation coefficient dropped dramatically passing through the Asian crisis and remained at the lowered level after that. Second, the Euro and the US dollar showed a strong negative correlation after 1997, implying that the prices of the two currencies moved in opposite directions. Third, we observed that Asian countries and Latin American countries moved away from the cluster center (USA) passing through the Asian crisis and Argentine crisis, respectively.

Dynamics of bounded confidence opinion in heterogeneous social networks: Concord against partial antagonism

Abstract: Bounded confidence models of opinion dynamics in social networks have been actively studied in recent years, in particular, opinion formation and extremism propagation along with other aspects of social dynamics. In this work, after an analysis of limitations of the Deffuant–Weisbuch (DW) bounded confidence, relative agreement model, we propose the mixed model that takes into account two psychological types of individuals. Concord agents (C-agents) are friendly people; they interact in a way that their opinions always get closer. Agents of the other psychological type show partial antagonism in their interaction (PA-agents). Opinion dynamics in heterogeneous social groups, consisting of agents of the two types, was studied on different social networks: Erdos–Renyi random graphs, small-world networks and complete graphs. Limit cases of the mixed model, pure C- and PA-societies, were also studied. We found that group opinion formation is, qualitatively, almost independent of the topology of networks used in this work. Opinion fragmentation, polarization and consensus are observed in the mixed model at different proportions of PA- and C-agents, depending on the value of initial opinion tolerance of agents. As for the opinion formation and arising of “dissidents”, the opinion dynamics of the C-agents society was found to be similar to that of the DW model, except for the rate of opinion convergence. Nevertheless, mixed societies showed dynamics and bifurcation patterns notably different to those of the DW model. The influence of biased initial conditions over opinion formation in heterogeneous social groups was also studied versus the initial value of opinion uncertainty, varying the proportion of the PA- to C-agents. Bifurcation diagrams showed an impressive evolution of collective opinion, in particular, radical changes of left to right consensus or vice versa at an opinion uncertainty value equal to 0.7 in the model with the PA/C mixture of population near 50/50.

Multifractal detrending moving average analysis on the US Dollar exchange rates

Abstract: In this paper, we investigate the multifractal behavior of the US dollar (USD) exchange rates. The results from the multifractal detrending moving average algorithm show that twelve exchange rate series were multifractal. The major source of multifractality are long-range correlations of small and large fluctuations. Fat-tail distributions have important effects on the multifractality of USD/AUR, USD/EUR and CNY/USD exchange rates. We also find evidence that extreme events play an important role in the contributions to multifractality for the USD/EUR exchange rate.

Solutions of the space-time fractional Cattaneo diffusion equation

Abstract: The object of this paper is to present the exact solution of the fractional Cattaneo equation for describing anomalous diffusion. The classical Cattaneo model has been generalised to the space-time fractional Cattaneo model. The method of the joint Laplace and Fourier transform is used in deriving the solution. The solutions of the fractional Cattaneo equation are obtained under integral and series forms in terms of the H -functions. Finally, the fractional order moments are also investigated.

Multifractal Fourier detrended cross-correlation analysis of traffic signals

Abstract: Multifractal detrended cross-correlation analysis (MF-DXA) has been developed to detect the long-range power-law cross-correlation of considered signals in the presence of non-stationarity. However, crossovers arising from extrinsic periodic trends make the scaling behavior difficult to analyze. We introduce a Fourier filtering method to eliminate the trend effects and systematically investigate the multifractal cross-correlation of simulated and real traffic signals. The crossover locations are found approximately corresponding to the periods of underlying trend. Traffic velocity on one road and flows on adjacent roads show strong cross-correlation. They also present weak multifractality after periodic trends are removed. The traffic velocity and flow are cross-correlated in opposite directions which is accordant to their actual evolution.

Topology of the correlation networks among major currencies using hierarchical structure methods

Abstract: We studied the topology of correlation networks among 34 major currencies using the concept of a minimal spanning tree and hierarchical tree for the full years of 2007–2008 when major economic turbulence occurred. We used the USD (US Dollar) and the TL (Turkish Lira) as numeraires in which the USD was the major currency and the TL was the minor currency. We derived a hierarchical organization and constructed minimal spanning trees (MSTs) and hierarchical trees (HTs) for the full years of 2007, 2008 and for the 2007–2008 period. We performed a technique to associate a value of reliability to the links of MSTs and HTs by using bootstrap replicas of data. We also used the average linkage cluster analysis for obtaining the hierarchical trees in the case of the TL as the numeraire. These trees are useful tools for understanding and detecting the global structure, taxonomy and hierarchy in financial data. We illustrated how the minimal spanning trees and their related hierarchical trees developed over a period of time. From these trees we identified different clusters of currencies according to their proximity and economic ties. The clustered structure of the currencies and the key currency in each cluster were obtained and we found that the clusters matched nicely with the geographical regions of corresponding countries in the world such as Asia or Europe. As expected the key currencies were generally those showing major economic activity.

Modified detrended fluctuation analysis based on empirical mode decomposition for the characterization of anti-persistent processes

Abstract: Detrended fluctuation analysis (DFA) is a simple but very efficient method for investigating the power-law long-term correlations of non-stationary time series, in which a detrending step is necessary to obtain the local fluctuations at different timescales. We propose to determine the local trends through empirical mode decomposition (EMD) and perform the detrending operation by removing the EMD-based local trends, which gives an EMD-based DFA method. Similarly, we also propose a modified multifractal DFA algorithm, called an EMD-based MFDFA. The performance of the EMD-based DFA and MFDFA methods is assessed with extensive numerical experiments based on fractional Brownian motion and multiplicative cascading process. We find that the EMD-based DFA method performs better than the classic DFA method in the determination of the Hurst index when the time series is strongly anticorrelated and the EMD-based MFDFA method outperforms the traditional MFDFA method when the moment order q of the detrended fluctuations is positive. We apply the EMD-based MFDFA to the 1 min data of Shanghai Stock Exchange Composite index, and the presence of multifractality is confirmed. We also analyze the daily Austrian electricity prices and confirm its anti-persistence.

Commodity predictability analysis with a permutation information theory approach

Abstract: It is widely known that commodity markets are not totally efficient. Long-range dependence is present, and thus the celebrated Brownian motion of prices can be considered only as a first approximation. In this work we analyzed the predictability in commodity markets by using a novel approach derived from Information Theory. The complexity–entropy causality plane has been recently shown to be a useful statistical tool to distinguish the stage of stock market development because differences between emergent and developed stock markets can be easily discriminated and visualized with this representation space [L. Zunino, M. Zanin, B.M. Tabak, D.G. Perez, O.A. Rosso, Complexity–entropy causality plane: a useful approach to quantify the stock market inefficiency, Physica A 389 (2010) 1891–1901]. By estimating the permutation entropy and permutation statistical complexity of twenty basic commodity future markets over a period of around 20 years (1991.01.02–2009.09.01), we can define an associated ranking of efficiency. This ranking is quantifying the presence of patterns and hidden structures in these prime markets. Moreover, the temporal evolution of the commodities in the complexity–entropy causality plane allows us to identify periods of time where the underlying dynamics is more or less predictable.

Visual angle model for car-following theory

Abstract: The vast majority of car-following models are lack of the consideration of human drivers’ characteristics. Based on the fact that each driver of a following vehicle perceives closing-in or shying-away a leading vehicle in front of him/her, primarily due to changes in the apparent size of the leading vehicle, we improved the full velocity difference (FVD) model and presented a visual angle car-following model. This model is in view of the stimulus–response framework and uses the visual angle and the change rate of the visual angle as stimulus. Results from linear analysis showed that the neutral stability line is asymmetry and the width of the leading vehicle has a great impact on the stability of traffic flow. Numerical simulations obtained the same results as theoretical analysis clearly such as density wave, shrinking hysteresis, asymmetry and wide scattering. Thus, the introducing of the visual angle can explain some complex nature of traffic flow and contribute to the design of more realistic car-following models.

Multifractal moving average analysis and test of multifractal model with tuned correlations

Abstract: We address two common major problems in the study of time series characterizing fluctuations in complex systems: multifractal analysis and multifractal modeling. Specifically, we introduce a multi-fractal centered moving average (MF-CMA) analysis, which is computationally easier but equivalently performing compared with the well-established multi-fractal detrended fluctuation analysis (MF-DFA) with linear detrending. In addition, we study in detail a generalized binomial multi-fractal model (GB-MFM) to conveniently and reliably generate multifractal surrogate data with arbitrary singularity strengths and arbitrary long-term persistence. We use the data generated by this model as well as realistic, by construction monofractal data series with crossovers and trends to test and compare the multifractal analysis methods and discuss finite-size effects as well as limitations due to spurious multifractality.

On spurious and corrupted multifractality: The effects of additive noise, short-term memory and periodic trends

Abstract: We study the performance of multifractal detrended fluctuation analysis (MF-DFA) applied to long-term correlated and multifractal data records in the presence of additive white noise, short-term memory and periodicities. Such additions and disturbances that can be typically found in the observational records of various complex systems ranging from climate dynamics to physiology, network traffic, and finance. In monofractal records, we find that (i) additive white noise hardly results in spurious multifractality, but causes underestimated generalized Hurst exponents h ( q ) for all q values; (ii) short-range correlations lead to pronounced crossovers in the generalized fluctuation functions F q ( s ) at positions that decrease with increasing moment q , thus causing significantly overestimated h ( q ) for small q and spurious multifractality; (iii) periodicities like seasonal trends (with standard deviations comparable with the one of the studied process) result in spurious “reversed” multifractality where h ( q ) increases with increasing q (except for very short time windows). We also show that in multifractal cascades moderate additions of noise, short-range memory, or periodic trends cause flawed results for h ( q ) with q 2 , while h ( q ) with q > 2 remains nearly unchanged.

Impact of the honk effect on the stability of traffic flow

Abstract: In this paper, we propose an extended car-following model which takes into account the honk effect. The analytical and numerical results show that the honk effect improves the stability of traffic flow. The dependence of the stability on the properties of the honk effect is investigated in this paper.