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1. | College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, 410082, China |
2. | College of Mathematics and Econometrics, Hunan University & Hunan Women's University, Changsha, Hunan, 410004 |
3. | Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J 1P3 |
References:
[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.
doi: 10.1137/090757290. |
[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.
doi: 10.1038/nature03236. |
[3] |
F. Cucker and S. Smale, Lectures on emergence, Japan J. Math., 2 (2007), 197-227.
doi: 10.1007/s11537-007-0647-x. |
[4] |
F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Trans. Automat. Control, 52 (2007), 852-862.
doi: 10.1109/TAC.2007.895842. |
[5] |
F. Cucker, S. Smale and D. Zhou, Modeling language evolution, Found. Comput. Math., 4 (2004), 315-343.
doi: 10.1007/s10208-003-0101-2. |
[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.
doi: 10.4310/CMS.2009.v7.n2.a2. |
[7] |
S. Y. Ha and E. Tadmor, From particle to kinetic and hydrodynamic descriptions of flocking, Kinet. Relat.Models, 1 (2008), 415-435.
doi: 10.3934/krm.2008.1.415. |
[8] |
Y. Liu and K. Passino, Stable social foraging swarms in a noisy environment, IEEE Trans. Automat. Control, 49 (2004), 30-44.
doi: 10.1109/TAC.2003.821416. |
[9] |
S. Motsch and E. Tadmor, A new model for Self-organized dynamics and its flocking behavior, J. Stat. Phys., 144 (2011), 923-947.
doi: 10.1007/s10955-011-0285-9. |
[10] |
C. W. Reynolds, Flocks, herds and schools: A distributed behavioral model, In: ACM SIGGRAPH Computer Graphics, 21 (1987), 25-34.
doi: 10.1145/37401.37406. |
[11] |
J. Shen, Cucker-Smale flocking under hierarchical leadership, SIAM J. Appl. Math., 68 (2008), 694-719.
doi: 10.1137/060673254. |
[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.
doi: 10.1137/S0036139903437424. |
[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.
doi: 10.1007/s11538-006-9088-6. |
[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.
doi: 10.1103/PhysRevLett.75.1226. |
show all references
References:
[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.
doi: 10.1137/090757290. |
[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.
doi: 10.1038/nature03236. |
[3] |
F. Cucker and S. Smale, Lectures on emergence, Japan J. Math., 2 (2007), 197-227.
doi: 10.1007/s11537-007-0647-x. |
[4] |
F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Trans. Automat. Control, 52 (2007), 852-862.
doi: 10.1109/TAC.2007.895842. |
[5] |
F. Cucker, S. Smale and D. Zhou, Modeling language evolution, Found. Comput. Math., 4 (2004), 315-343.
doi: 10.1007/s10208-003-0101-2. |
[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.
doi: 10.4310/CMS.2009.v7.n2.a2. |
[7] |
S. Y. Ha and E. Tadmor, From particle to kinetic and hydrodynamic descriptions of flocking, Kinet. Relat.Models, 1 (2008), 415-435.
doi: 10.3934/krm.2008.1.415. |
[8] |
Y. Liu and K. Passino, Stable social foraging swarms in a noisy environment, IEEE Trans. Automat. Control, 49 (2004), 30-44.
doi: 10.1109/TAC.2003.821416. |
[9] |
S. Motsch and E. Tadmor, A new model for Self-organized dynamics and its flocking behavior, J. Stat. Phys., 144 (2011), 923-947.
doi: 10.1007/s10955-011-0285-9. |
[10] |
C. W. Reynolds, Flocks, herds and schools: A distributed behavioral model, In: ACM SIGGRAPH Computer Graphics, 21 (1987), 25-34.
doi: 10.1145/37401.37406. |
[11] |
J. Shen, Cucker-Smale flocking under hierarchical leadership, SIAM J. Appl. Math., 68 (2008), 694-719.
doi: 10.1137/060673254. |
[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.
doi: 10.1137/S0036139903437424. |
[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.
doi: 10.1007/s11538-006-9088-6. |
[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.
doi: 10.1103/PhysRevLett.75.1226. |
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