Please wait a minute...
Chin. Phys. B, 2016, Vol. 25(5): 050505    DOI: 10.1088/1674-1056/25/5/050505
GENERAL Prev   Next  

Dynamic properties of chasers in a moving queue based on a delayed chasing model

Ning Guo(郭宁)1, Jian-Xun Ding(丁建勋)2,3, Xiang Ling(凌翔)2, Qin Shi(石琴)2, Reinhart Kühne2,4
1. School of Engineering Science, University of Science and Technology of China, Hefei 230026, China;
2. School of Transportation Engineering, Hefei University of Technology, Hefei 230009, China;
3. Key Laboratory of Process Optimization and Intelligent Decision-Making of Ministry of Education, Hefei 230009, China;
4. Department for Transportation, University of Stuttgart, Stuttgart 70174, Germany
Abstract  A delayed chasing model is proposed to simulate the chase behavior in the queue, where each member regards the closest one ahead as the target, and the leader is attracted to a target point with slight fluctuation. When the initial distances between neighbors possess an identical low value, the fluctuating target of the leader can cause an amplified disturbance in the queue. After a long period of time, the queue recovers the stable state from the disturbance, forming a straight-line-like pattern again, but distances between neighbors grow. Whether the queue can keep stable or not depends on initial distance, desired velocity, and relaxation time. Furthermore, we carry out convergence analysis to explain the divergence transformation behavior and confirm the convergence conditions, which is in approximate agreement with simulations.
Keywords:  chase queue      disturbance      convergence analysis  
Received:  28 October 2015      Revised:  18 January 2016      Published:  05 May 2016
PACS:  05.65.+b (Self-organized systems)  
  89.75.-k (Complex systems)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 71071044, 71001001, 71201041, and 11247291), the Doctoral Program of the Ministry of Education of China (Grant Nos. 20110111120023 and 20120111120022), the Postdoctoral Fund Project of China (Grant No. 2013M530295), the National Basic Research Program of China (Grant No. 2012CB725404), and 1000 Plan for Foreign Talent, China (Grant No. WQ20123400070).
Corresponding Authors:  Ning Guo     E-mail:

Cite this article: 

Ning Guo(郭宁), Jian-Xun Ding(丁建勋), Xiang Ling(凌翔), Qin Shi(石琴), Reinhart Kühne Dynamic properties of chasers in a moving queue based on a delayed chasing model 2016 Chin. Phys. B 25 050505

[1] Zhang H and Chen Z 2014 IEEE Trans. Neural Netw. Learn. Syst. 25 1921
[2] Wang J, He Z and Wang J 2015 Chin. Phys. B 24 060101
[3] Wang X, Guo W and Zheng X 2015 Chin. Phys. B 24 070504
[4] Xu Y, Huang H J and Yong G 2012 Chin. Phys. Lett. 29 080502
[5] Ferrari-Trecate G, Galbusera L, Marciandi M and Scattolini R 2009 IEEE Tran. Autom. Control 54 2560
[6] Franco E, Magni L, Parisini T, Polycarpou M and Raimondo D 2008 IEEE Tran. Autom. Control 53 324
[7] Zhan J and Li X 2013 Automatica 49 2502
[8] Cheng Z, Zhang H, Fan M and Chen G 2015 IEEE Tran. Circuits Syst. I 62 825
[9] Chowdhury D, Santen L and Schadschneider A 2000 Phys. Rep. 329 199
[10] Helbing D 2001 Rev. Mod. Phys. 73 1067
[11] Vicsek T and Zafiris A 2010 arXiv:1010.5017
[12] Isaacs R 1965 Differential Games (New York: Wiley) p. 512
[13] Basar T and Olsder G L 1999 Dynamic Noncooperative Game Theory (Philadelphia: SIAM) p. 459
[14] Nahin P J 2007 Chases and Escapes: The Mathematics of Pursuit and Evasion (Princeton University Press) p. 352
[15] Krapivsky P L and Redner S 1996 J. Phys. A: Math. Gen. 29 5347
[16] Oshanin G, Vasilyev O, Krapivsky P L and Klafter J 2009 Proc. Natl. Acad. Sci. 106 13696
[17] Hespanha J P, Kim H J and Sastry S 1999 38th IEEE Conference on Decision and Control, 1999 Phoenix, USA, p. 2432
[18] Vidal R, Shakernia O, Kim J H, Shim D H and Sastry S 2002 IEEE Trans. Robot. Autom. 18 662
[19] Kamimura A and Ohira T 2010 New J. Phys. 12 053013
[20] Nishi R, Kamimura A, Nishinari K and Ohira T 2012 Phys. A 391 337
[21] Iwama T and Sato M 2012 Phys. Rev. E 86 067102
[22] Helbing D and Molnar P 1995 Phys. Rev. E 51 4282
[23] Helbing D, Farkas I and Vicsek T 2000 Nature 407 487
[24] Moussaid M, Helbing D, Garnier S, Johansson A, Combe M and Theraulaz G 2009 Proc. Roy. Soc. B 276 2755
[1] A two-dimensional quantum walk driven by a single two-side coin
Quan Lin(林泉), Hao Qin(秦豪) Kun-Kun Wang(王坤坤), Lei Xiao(肖磊), and Peng Xue(薛鹏). Chin. Phys. B, 2020, 29(11): 110303.
[2] Influence of warm eddies on sound propagation in the Gulf of Mexico
Yao Xiao(肖瑶), Zhenglin Li(李整林), Jun Li(李鋆), Jiaqi Liu(刘佳琪), Karim G Sabra. Chin. Phys. B, 2019, 28(5): 054301.
[3] Traffic flow velocity disturbance characteristics and control strategy at the bottleneck of expressway
Jun-Wei Zeng(曾俊伟), Yong-Sheng Qian(钱勇生), Xu-Ting Wei(魏谞婷), Xiao Feng(冯骁). Chin. Phys. B, 2018, 27(12): 124502.
[4] Effect of stochastic electromagnetic disturbances on autapse neuronal systems
Liang-Hui Qu(曲良辉), Lin Du(都琳), Zi-Chen Deng(邓子辰), Zi-Lu Cao(曹子露), Hai-Wei Hu(胡海威). Chin. Phys. B, 2018, 27(11): 118707.
[5] Nonlinear control of spacecraft formation flying with disturbance rejection and collision avoidance
Qing Ni(倪庆), Yi-Yong Huang(黄奕勇), Xiao-Qian Chen(陈小前). Chin. Phys. B, 2017, 26(1): 014502.
[6] A local energy-preserving scheme for Klein–Gordon–Schrödinger equations
Cai Jia-Xiang, Wang Jia-Lin, Wang Yu-Shun. Chin. Phys. B, 2015, 24(5): 050205.
[7] Function projective synchronization between two different complex networks with correlated random disturbances
Jin Yun-Guo, Zhong Shou-Ming, An Na. Chin. Phys. B, 2015, 24(4): 049202.
[8] Quantum correlations in a two-qubit anisotropic Heisenberg XYZ chain with uniform magnetic field
Li Lei, Yang Guo-Hui. Chin. Phys. B, 2014, 23(7): 070306.
[9] Thermal quantum and total correlations in spin-1 bipartite system
Qiu Liang, Ye Bin. Chin. Phys. B, 2014, 23(5): 050304.
[10] Measurement-induced disturbance in Heisenberg XY spin model with Dzialoshinskii-Moriya interaction under intrinsic decoherence
Shen Cheng-Gao, Zhang Guo-Feng, Fan Kai-Ming, Zhu Han-Jie. Chin. Phys. B, 2014, 23(5): 050310.
[11] Correlation dynamics of a qubit–qutrit system in a spin-chain environment with Dzyaloshinsky–Moriya interaction
Yang Yang, Wang An-Min. Chin. Phys. B, 2014, 23(2): 020307.
[12] Effect of electromagnetic disturbance on thepractical QKD system in the smart grid
Li Fang-Yi, Wang Dong, Wang Shuang, Li Mo, Yin Zhen-Qiang, Li Hong-Wei, Chen Wei, Han Zheng-Fu. Chin. Phys. B, 2014, 23(12): 124201.
[13] Quantum correlation switches for dipole arrays
Li Yan-Jie, Liu Jin-Ming, Zhang Yan. Chin. Phys. B, 2014, 23(11): 110306.
[14] Measurement-induced disturbance between two atoms in Tavis–Cummings model with dipole–dipole interaction
Zhang Guo-Feng, Wang Xiao, Lü Guang-Hong. Chin. Phys. B, 2014, 23(10): 104204.
[15] Study of typical space wave-particle coupling eventspossibly related with seismic activity
Zhang Zhen-Xia, Wang Chen-Yu, Shen Xu-Hui, Li Xin-Qiao, Wu Shu-Gui. Chin. Phys. B, 2014, 23(10): 109401.
No Suggested Reading articles found!