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Weak-Painlevé property and integrability of general dynamical systems
Effectual leadership in flocks with hierarchy and individual preference
1. | Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China |
References:
[1] |
S. Ahn, H.-O. Bae, S.-Y. Ha, Y. Kim and H. Lim, Application of flocking mechanism to the modeling of stochastic volatility, Math. Models Methods Appl. Sci., 23 (2013), 1603-1628.
doi: 10.1142/S0218202513500176. |
[2] |
S. Ahn, H. Choi, S.-Y. Ha and H. Lee, On collision-avoiding initial configurations to Cucker-Smale type flocking models, Comm. Math. Sci., 10 (2012), 625-643.
doi: 10.4310/CMS.2012.v10.n2.a10. |
[3] |
S. Ahn and S.-Y. Ha, Stochastic flocking dynamics of the Cucker-Smale model with multiplicative white noises, J. Math. Phys., 51 (2010), 103301.
doi: 10.1063/1.3496895. |
[4] |
H. Bae, Y.-P. Choi, S.-Y. Ha and M. Kang, Time-asymptotic interaction of flocking particles and an incompressible viscous fluid, Nonlinearity, 25 (2012), 1155-1177.
doi: 10.1088/0951-7715/25/4/1155. |
[5] |
M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale and V. Zdravkovic, Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study, Proc. Nat. Acad. Sci., 105 (2008), 1232-1237.
doi: 10.1073/pnas.0711437105. |
[6] |
N. Bellomo, H. Beresticky, F. Brezzi and J. P. Nadal, Mathematics and complexity in life and human sciences, Math. Models Methods Appl. Sci., 20 (2010), 1391-1395.
doi: 10.1142/S0218202510004702. |
[7] |
N. Bellomo and F. Brezzi, Mathematics and complexity of multi-particle systems, Math. Models Methods Appl. Sci., 22 (2012), 1103001.
doi: 10.1142/S0218202511030011. |
[8] |
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. |
[9] |
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. |
[10] |
F. Cucker and J.-G. Dong, On the critical exponent for flocks under hierarchical leadership, Math. Models Methods in Appl. Sci., 19 (2009), 1391-1404.
doi: 10.1142/S0218202509003851. |
[11] |
F. Cucker and J.-G. Dong, Avoiding collisions in flocks, IEEE Trans. Automat. Control, 55 (2010), 1238-1243.
doi: 10.1109/TAC.2010.2042355. |
[12] |
F. Cucker and C. Huepe, Flocking with informed agents, MathS in Action, 1 (2008), 1-25.
doi: 10.5802/msia.1. |
[13] |
F. Cucker and E. Mordecki, Flocking in noisy environments, J. Math. Pures Appl., 89 (2008), 278-296.
doi: 10.1016/j.matpur.2007.12.002. |
[14] |
F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Trans. Automat. Control, 52 (2007), 852-862.
doi: 10.1109/TAC.2007.895842. |
[15] |
F. Cucker and S. Smale, On the mathematics of emergence, Japan. J. Math., 2 (2007), 197-227.
doi: 10.1007/s11537-007-0647-x. |
[16] |
F. Dalmao and E. Mordecki, Cucker-Smale flocking under hierarchical leadership and random interactions, SIAM J. Appl. Math., 71 (2010), 1307-1316.
doi: 10.1137/100785910. |
[17] |
R. Duan, M. Fornasier and G. Toscani, A kinetic flocking model with diffusion, Comm. Math. Phys., 300 (2010), 95-145.
doi: 10.1007/s00220-010-1110-z. |
[18] |
M. Fornasier, J. Haskovec and G. Toscani, Fluid dynamic description of flocking via the Povzner-Boltzmann equation, Phys. D, 240 (2011), 21-31.
doi: 10.1016/j.physd.2010.08.003. |
[19] |
S.-Y. Ha, K. Lee and D. Levy, Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system, Comm. Math. Sci., 7 (2009), 453-469.
doi: 10.4310/CMS.2009.v7.n2.a9. |
[20] |
S.-Y. Ha and Z. Li, Complete synchronization of Kuramoto oscillators with hierarchical leadership, Comm. Math. Sci., 12 (2014), 485-508.
doi: 10.4310/CMS.2014.v12.n3.a5. |
[21] |
S.-Y. Ha and J.-G. Liu, A simple proof of the Cucker-Smale flocking dynamics and mean field limit, Comm. Math. Sci., 7 (2009), 297-325.
doi: 10.4310/CMS.2009.v7.n2.a2. |
[22] |
S.-Y. Ha and E. Tadmor, From particle to kinetic and hydrodynamic description of flocking, Kinet. Relat. Mod., 1 (2008), 415-435.
doi: 10.3934/krm.2008.1.415. |
[23] |
R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 2013. |
[24] |
A. Jadbabaie, J. Lin and A. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. Automat. Control, 48 (2003), 988-1001.
doi: 10.1109/TAC.2003.812781. |
[25] |
N. E. Leonard, D. A. Paley, F. Lekien, R. Sepulchre, D. M. Fratantoni and R. E. Davis, Collective motion, sensor networks and ocean sampling, Proc. IEEE, 95 (2007), 48-74.
doi: 10.1109/JPROC.2006.887295. |
[26] |
Z. Li and S.-Y. Ha, On the Cucker-Smale flocking with alternating leaders, submitted to Quart. Appl. Math. |
[27] |
Z. Li, S.-Y. Ha and X. Xue, Emergent phenomena in an ensemble of Cucker-Smale particles under joint rooted leadership, Math. Models Methods Appl. Sci., 2013.
doi: 10.1142/S0218202514500043. |
[28] |
Z. Li and X. Xue, Cucker-Smale flocking under rooted leadership with fixed and switching topologies, SIAM J. Appl. Math., 70 (2010), 3156-3174.
doi: 10.1137/100791774. |
[29] |
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. |
[30] |
M. Nagy, Z. Ákos, D. Biro and T. Vicsek, Hierarchical group dynamics in pigeon flocks, Nature, 464 (2010), 890-893.
doi: 10.1038/nature08891. |
[31] |
J. Park, H. Kim and S.-Y. Ha, Cucker-Smale flocking with inter-particle bonding forces, IEEE Trans. Automat. Control, 55 (2010), 2617-2623.
doi: 10.1109/TAC.2010.2061070. |
[32] |
L. Perea, P. Elosegui and G. Gómez, Extension of the Cucker-Smale control law to space flight formation, J. Guid. Control Dynam., 32 (2009), 527-537.
doi: 10.2514/1.36269. |
[33] |
J. Shen, Cucker-Smale flocking under hierarchical leadership, SIAM J. Appl. Math., 68 (2007/08), 694-719.
doi: 10.1137/060673254. |
[34] |
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. |
[35] |
T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen and O. Schochet, Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett., 75 (1995), 1226-1229.
doi: 10.1103/PhysRevLett.75.1226. |
show all references
References:
[1] |
S. Ahn, H.-O. Bae, S.-Y. Ha, Y. Kim and H. Lim, Application of flocking mechanism to the modeling of stochastic volatility, Math. Models Methods Appl. Sci., 23 (2013), 1603-1628.
doi: 10.1142/S0218202513500176. |
[2] |
S. Ahn, H. Choi, S.-Y. Ha and H. Lee, On collision-avoiding initial configurations to Cucker-Smale type flocking models, Comm. Math. Sci., 10 (2012), 625-643.
doi: 10.4310/CMS.2012.v10.n2.a10. |
[3] |
S. Ahn and S.-Y. Ha, Stochastic flocking dynamics of the Cucker-Smale model with multiplicative white noises, J. Math. Phys., 51 (2010), 103301.
doi: 10.1063/1.3496895. |
[4] |
H. Bae, Y.-P. Choi, S.-Y. Ha and M. Kang, Time-asymptotic interaction of flocking particles and an incompressible viscous fluid, Nonlinearity, 25 (2012), 1155-1177.
doi: 10.1088/0951-7715/25/4/1155. |
[5] |
M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale and V. Zdravkovic, Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study, Proc. Nat. Acad. Sci., 105 (2008), 1232-1237.
doi: 10.1073/pnas.0711437105. |
[6] |
N. Bellomo, H. Beresticky, F. Brezzi and J. P. Nadal, Mathematics and complexity in life and human sciences, Math. Models Methods Appl. Sci., 20 (2010), 1391-1395.
doi: 10.1142/S0218202510004702. |
[7] |
N. Bellomo and F. Brezzi, Mathematics and complexity of multi-particle systems, Math. Models Methods Appl. Sci., 22 (2012), 1103001.
doi: 10.1142/S0218202511030011. |
[8] |
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. |
[9] |
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. |
[10] |
F. Cucker and J.-G. Dong, On the critical exponent for flocks under hierarchical leadership, Math. Models Methods in Appl. Sci., 19 (2009), 1391-1404.
doi: 10.1142/S0218202509003851. |
[11] |
F. Cucker and J.-G. Dong, Avoiding collisions in flocks, IEEE Trans. Automat. Control, 55 (2010), 1238-1243.
doi: 10.1109/TAC.2010.2042355. |
[12] |
F. Cucker and C. Huepe, Flocking with informed agents, MathS in Action, 1 (2008), 1-25.
doi: 10.5802/msia.1. |
[13] |
F. Cucker and E. Mordecki, Flocking in noisy environments, J. Math. Pures Appl., 89 (2008), 278-296.
doi: 10.1016/j.matpur.2007.12.002. |
[14] |
F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Trans. Automat. Control, 52 (2007), 852-862.
doi: 10.1109/TAC.2007.895842. |
[15] |
F. Cucker and S. Smale, On the mathematics of emergence, Japan. J. Math., 2 (2007), 197-227.
doi: 10.1007/s11537-007-0647-x. |
[16] |
F. Dalmao and E. Mordecki, Cucker-Smale flocking under hierarchical leadership and random interactions, SIAM J. Appl. Math., 71 (2010), 1307-1316.
doi: 10.1137/100785910. |
[17] |
R. Duan, M. Fornasier and G. Toscani, A kinetic flocking model with diffusion, Comm. Math. Phys., 300 (2010), 95-145.
doi: 10.1007/s00220-010-1110-z. |
[18] |
M. Fornasier, J. Haskovec and G. Toscani, Fluid dynamic description of flocking via the Povzner-Boltzmann equation, Phys. D, 240 (2011), 21-31.
doi: 10.1016/j.physd.2010.08.003. |
[19] |
S.-Y. Ha, K. Lee and D. Levy, Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system, Comm. Math. Sci., 7 (2009), 453-469.
doi: 10.4310/CMS.2009.v7.n2.a9. |
[20] |
S.-Y. Ha and Z. Li, Complete synchronization of Kuramoto oscillators with hierarchical leadership, Comm. Math. Sci., 12 (2014), 485-508.
doi: 10.4310/CMS.2014.v12.n3.a5. |
[21] |
S.-Y. Ha and J.-G. Liu, A simple proof of the Cucker-Smale flocking dynamics and mean field limit, Comm. Math. Sci., 7 (2009), 297-325.
doi: 10.4310/CMS.2009.v7.n2.a2. |
[22] |
S.-Y. Ha and E. Tadmor, From particle to kinetic and hydrodynamic description of flocking, Kinet. Relat. Mod., 1 (2008), 415-435.
doi: 10.3934/krm.2008.1.415. |
[23] |
R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 2013. |
[24] |
A. Jadbabaie, J. Lin and A. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. Automat. Control, 48 (2003), 988-1001.
doi: 10.1109/TAC.2003.812781. |
[25] |
N. E. Leonard, D. A. Paley, F. Lekien, R. Sepulchre, D. M. Fratantoni and R. E. Davis, Collective motion, sensor networks and ocean sampling, Proc. IEEE, 95 (2007), 48-74.
doi: 10.1109/JPROC.2006.887295. |
[26] |
Z. Li and S.-Y. Ha, On the Cucker-Smale flocking with alternating leaders, submitted to Quart. Appl. Math. |
[27] |
Z. Li, S.-Y. Ha and X. Xue, Emergent phenomena in an ensemble of Cucker-Smale particles under joint rooted leadership, Math. Models Methods Appl. Sci., 2013.
doi: 10.1142/S0218202514500043. |
[28] |
Z. Li and X. Xue, Cucker-Smale flocking under rooted leadership with fixed and switching topologies, SIAM J. Appl. Math., 70 (2010), 3156-3174.
doi: 10.1137/100791774. |
[29] |
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. |
[30] |
M. Nagy, Z. Ákos, D. Biro and T. Vicsek, Hierarchical group dynamics in pigeon flocks, Nature, 464 (2010), 890-893.
doi: 10.1038/nature08891. |
[31] |
J. Park, H. Kim and S.-Y. Ha, Cucker-Smale flocking with inter-particle bonding forces, IEEE Trans. Automat. Control, 55 (2010), 2617-2623.
doi: 10.1109/TAC.2010.2061070. |
[32] |
L. Perea, P. Elosegui and G. Gómez, Extension of the Cucker-Smale control law to space flight formation, J. Guid. Control Dynam., 32 (2009), 527-537.
doi: 10.2514/1.36269. |
[33] |
J. Shen, Cucker-Smale flocking under hierarchical leadership, SIAM J. Appl. Math., 68 (2007/08), 694-719.
doi: 10.1137/060673254. |
[34] |
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. |
[35] |
T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen and O. Schochet, Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett., 75 (1995), 1226-1229.
doi: 10.1103/PhysRevLett.75.1226. |
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