JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (12): 114-119.doi: 10.6040/j.issn.1671-9352.0.2017.504

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Flocking under hierarchical leadership with white noise

WU Chen, JIN Ying-hua*, WANG Shi-li   

  1. School of Science, Jiangnan University, Wuxi 214122, Jiangsu, China
  • Online:2018-12-20 Published:2018-12-18

Abstract: The flocking under hierarchical leadership with white noise was mainly studied. First we proposed a model with white noise under the hierarchical leadership, and then use the properties of Itô formula, mathematical induction and mathematical expectation function to prove that when the noise intensity satisfies certain conditions and the time tends to infinity, the hierarchical group can reach the flocking. Finally, an example of state diagram and error graph after cluster is affected by noise is given by numerical simulation. The experimental results demonstrate the correctness of the conclusions.

Key words: flocking, hierarchical leadership, white noise, mathematical induction

CLC Number: 

  • TP13
[1] BREDER C M. Equations descriptive of fish schools and other animal aggregations[J]. Ecology, 1954, 35:361-370.
[2] RU Lining, LI Zhuchun, XUE Xiaoping. Cucker-Smale flocking with randomly failed interactions[J]. Journal of the Franklin Institute, 2015, 352(3):1099-1118.
[3] LIU Yicheng, WU Jianhong. Flocking and asymptotic velocity of the Cucker-Smale model with processing delay[J]. Journal of Mathematical Analysis and Applica-tions, 2014, 415(1):53-61.
[4] AHN S, BAE H-O, HA S-Y, et al. Application of flocking mechanism to the modeling of stochastic volatility[J]. Math Models Methods Appl Sci, 2013, 23(9):1603-1628.
[5] YANG Zhengquan, ZHANG Qing, JIANG Zuolian, et al. Flocking of multi-agents with time delay[J]. International Journal of Systems Science, 2012, 43(11):2125-2134.
[6] RU Lining, LI Zhuchun, XUE Xiaoping. Cucker-Smale flocking with randomly failed interactions[J]. Journal of the Franklin Institute, 2015, 352(3):1099-1118.
[7] TANNER H, JADBABAIE A, PAPPAS G. Flocking in fixed and switching networks[J]. IEEE Transactions on Automatic Control, 2007, 52(5):863-868.
[8] CUCKER F, MORDECKI E. Flocking in noisy environment[J]. J Math Pures Appl, 2008, 89:278-296.
[9] HA S-Y, LIU J-G. A simple proof of Cucker-Smale focking dynamics and mean field limit[J]. Commun Math Sci, 2009, 7:297-325.
[10] HA S-Y, TADMOR E. From particle to kinetic and hydrodynamic description of flocking[J]. Kinetic Relat Models, 2008, 1(3):415-435.
[11] AHN S, CHOI H, HA S-Y, et al. On the collision avoiding initial configurations to the Cucker-Smale type flocking models[J]. Commun Math Sci, 2012, 10:625-643.
[12] AHN S, HA S-Y. Stochastic flocking dynamics of the Cucker-Smale model with multiplicative white noises[J]. Journal of Mathematical Physics, 2010, 51:103301.
[13] CHO J, HA S-Y, HUANG F, et al. Emergence of bicluster flocking for agent-based models with unit speed constraint[J]. Analysis and Applications, 2016, 14(1):39-73.
[14] REYNOLDS C W. Flocks, herds, and schools: a distributed behavioral model[J]. Computer Graphics, 1987, 21:25-34.
[15] VICSEK T, CZIROK A, BEN-JACOB E, et al. Novel type of phase transition in a system of self-driven particles[J]. Physical Review Letters, 1995, 75:1226-1229.
[16] CUCKER F, SMALE S. Emergent behavior in flocks[J]. IEEE Transactions on Automatic Control, 2007, 52(5):852-862.
[17] CUCKER F, SMALE S. On the mathematics of emergence[J]. Japanese Journal of Mathematics, 2007, 2(1):197-227.
[18] SHEN J. Cucker-Smale flocking under hierarchical leadership[J]. Appl Math, 2007, 68:694-719.
[19] CUCKER F, DONG J G. A general collision-avoiding flocking framework[J]. IEEE Transactions on Automatic Control, 2011, 56(5):1124-1128.
[20] DONG J. Flocking under hierarchical leadership with a free-will leader[J]. International Journal Robust Non-linear Control, 2013, 23:1891-1898.
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