`a`
Mathematical Biosciences and Engineering (MBE)
 

Flocking and invariance of velocity angles
Pages: 369 - 380, Issue 2, April 2016

doi:10.3934/mbe.2015007      Abstract        References        Full text (334.9K)           Related Articles

Le Li - College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, 410082, China (email)
Lihong Huang - College of Mathematics and Econometrics, Hunan University & Hunan Women's University, Changsha, Hunan, 410004, China (email)
Jianhong Wu - Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J 1P3, Canada (email)

1 J. A. Carrillo, M. Fornasier, J. Rosado and G. Toscani, Asymptotic flocking dynamics for the kinetic Cucker-Smale model, SIAM J. Math. Anal., 42 (2010), 218-236.       
2 I. D. Couzin, J. Krause, N. R. Franks and S. Levin, Effective leadership and decision making in animal groups on the move, Nature, 433 (2005), 513-516.
3 F. Cucker and S. Smale, Lectures on emergence, Japan J. Math., 2 (2007), 197-227.       
4 F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Trans. Automat. Control, 52 (2007), 852-862.       
5 F. Cucker, S. Smale and D. Zhou, Modeling language evolution, Found. Comput. Math., 4 (2004), 315-343.       
6 S. Y. Ha and J. G. Liu, A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, Commun. Math. Sci., 7 (2009), 297-325.       
7 S. Y. Ha and E. Tadmor, From particle to kinetic and hydrodynamic descriptions of flocking, Kinet. Relat.Models, 1 (2008), 415-435.       
8 Y. Liu and K. Passino, Stable social foraging swarms in a noisy environment, IEEE Trans. Automat. Control, 49 (2004), 30-44.       
9 S. Motsch and E. Tadmor, A new model for Self-organized dynamics and its flocking behavior, J. Stat. Phys., 144 (2011), 923-947.       
10 C. W. Reynolds, Flocks, herds and schools: A distributed behavioral model, In: ACM SIGGRAPH Computer Graphics, 21 (1987), 25-34.
11 J. Shen, Cucker-Smale flocking under hierarchical leadership, SIAM J. Appl. Math., 68 (2008), 694-719.       
12 C. M. Topaz and A. L. Bertozzi, Swarming patterns in a two-dimensional kinematic model for biological groups, SIAM J. Appl. Math., 65 (2004), 152-174.       
13 C. M. Topaz, A. L. Bertozzi and M. A. Lewis, A nonlocal continuum model for biological aggregation, Bull. Math. Bio., 68 (2006), 1601-1623.       
14 T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen and O. Shochet, Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett., 75 (1995), 1226-1225.

Go to top