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Cascade flocking with free-will
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, China |
3. | Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3 |
References:
[1] |
A. Flack, B. Pettit and R. Freeman, What are leaders made of? The role of individual experience in determining leader-follower relations in homing pigeons, Animal Behaviour, 83 (2012), 703-709.
doi: 10.1016/j.anbehav.2011.12.018. |
[2] |
A. Flack, B. Pettit and R. Freeman, Fault-tolerant flocking for a group of autonomous mobile robots, The Journal of Systems and Software, 84 (2011), 29-36. |
[3] |
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. |
[4] |
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. |
[5] |
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. |
[6] |
D. Gu and Z. Wang, Leader-Follower flocking: Algorithms and experiments, PNAS, 17 (2008), 1211-1219. |
[7] |
D. Gu and Z. Wang, Leader-follower flocking: Algorithms and experiments, IEEE Transactions on control systems technology, 17 (2009), 1211-1219. |
[8] |
D. J. Hoare, I. D. Couzin, J.-G. J. Godin and J. Krause, Context-dependent group size choice in fish, Animal Behaviour, 67 (2007), 155-164.
doi: 10.1016/j.anbehav.2003.04.004. |
[9] |
F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Trans. Automat. Control, 52 (2007), 852-862.
doi: 10.1109/TAC.2007.895842. |
[10] |
F. Cucker and S. Smale, Lectures on emergence, Japan J. Math., 2 (2007), 197-227.
doi: 10.1007/s11537-007-0647-x. |
[11] |
F. Cucker, S. Smale and D. Zhou, Modeling language evolution, Found. Comput. Math., 4 (2004), 315-343.
doi: 10.1007/s10208-003-0101-2. |
[12] |
F. Cucker and C. Huepe, Flocking with informed agents, Mathematics In Action, 1 (2008), 1-25.
doi: 10.5802/msia.1. |
[13] |
F. Dalmao and E. Mordecki, Cucker-Smale flocking under hierachical leadership and random interactions, SIAM J. Aappl. Math., 71 (2011), 1307-1316.
doi: 10.1137/100785910. |
[14] |
G. Grgoire, H. Chat and Y. Tu, Moving and staying together without a leader, Physica D, 181 (2003), 157-170.
doi: 10.1016/S0167-2789(03)00102-7. |
[15] |
H. Su, X. Wang and Z. Lin, Flocking of multi-agents with a virtual leader, IEEE Transactions on automatic control, 54 (2009), 293-307.
doi: 10.1109/TAC.2008.2010897. |
[16] |
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. |
[17] |
I. Couzin, J. Krause, R. James and G. Ruxton, Collective memory and spatial sorting in animal groups, J. theor. Biol., 218 (2002), 1-11.
doi: 10.1006/jtbi.2002.3065. |
[18] |
I. D. Couzin, J. Krause, R. James and G. D. Ruxton, Complex spatial group patterns result from different animal communication mechanisms, PNAS, 104 (2007), 6974-6979. |
[19] |
J. A. Carrillo, M. Fornasier, J. Rosado and G. Toscani, Asymptotic flocking dynamics for the kinetic Cuker-Smale model, SIAM J. Math. Anal., 42 (2010), 218-236.
doi: 10.1137/090757290. |
[20] |
J. Dong, Flocking under hierarchical leadership with a free-will leader, International journal of robust and nonlinear control, 23 (2013), 1891-1898. |
[21] |
J. Shen, Cucker-Smale flocking under hierarchical leadership, SIAM J. Appl. Math., 68 (2008), 694-719.
doi: 10.1137/060673254. |
[22] |
M. Agueh, R. Illner and A. Richardson, Analysis and simulations of a refined flocking and swarming model of Cuker-Smale type, Kinetic and Related Models, 4 (2011), 1-16.
doi: 10.3934/krm.2011.4.1. |
[23] |
M. Ballerini, N. Cabibbo, R. Candelier and et al., Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study, PNAS, 105 (2008), 1232-1237.
doi: 10.1073/pnas.0711437105. |
[24] |
M. Nagy, Z. Akos, D. Biro and T. Vicsek, Hierarchical group dynamics in pigeon flocks, Nature, 464 (2010), 890-894.
doi: 10.1038/nature08891. |
[25] |
S. Ha and J. 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. |
[26] |
S. 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. |
[27] |
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. |
[28] |
S. Motsch and E. Tadmor, Asymptotic flocking dynamics for the kinetic Cucker-Smale model, SIAM REVIEW, 56 (2014), 577-621.
doi: 10.1137/120901866. |
[29] |
T. Vicsek, A. Czirk, 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), 1226-1235.
doi: 10.1103/PhysRevLett.75.1226. |
[30] |
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. |
[31] |
Z. Akos, T. Vicsek and E. Kubinyi, Leadership and path characteristics during walks are linked to dominance order and individual traits in Dogs, Computational biology, 10 (2014), 1-9. |
[32] |
Z. Li and X. Xue, Cucher-Smale flocking under rooted leadership with fixed switching topologies, SIAM J. Appl. Math., 70 (2010), 3156-3174.
doi: 10.1137/100791774. |
[33] |
Z. Li and X. Xue, Cucker-Smale flocking under rooted leadership with free-will agents, Physica A, 410 (2014), 205-217.
doi: 10.1016/j.physa.2014.05.008. |
[34] |
Z. Li, Effectual leadership in flocks with hierarchy and individual preference, Discrete and Continue Dynamical Systems, 34 (2014), 3683-3702.
doi: 10.3934/dcds.2014.34.3683. |
[35] |
Z. Wang and D. Gu, A local sensor based leader-follower flocking system, in Proc. 2008 IEEE Int. Conf. Robot. Autom., (2008), 19-23. |
show all references
References:
[1] |
A. Flack, B. Pettit and R. Freeman, What are leaders made of? The role of individual experience in determining leader-follower relations in homing pigeons, Animal Behaviour, 83 (2012), 703-709.
doi: 10.1016/j.anbehav.2011.12.018. |
[2] |
A. Flack, B. Pettit and R. Freeman, Fault-tolerant flocking for a group of autonomous mobile robots, The Journal of Systems and Software, 84 (2011), 29-36. |
[3] |
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. |
[4] |
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. |
[5] |
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. |
[6] |
D. Gu and Z. Wang, Leader-Follower flocking: Algorithms and experiments, PNAS, 17 (2008), 1211-1219. |
[7] |
D. Gu and Z. Wang, Leader-follower flocking: Algorithms and experiments, IEEE Transactions on control systems technology, 17 (2009), 1211-1219. |
[8] |
D. J. Hoare, I. D. Couzin, J.-G. J. Godin and J. Krause, Context-dependent group size choice in fish, Animal Behaviour, 67 (2007), 155-164.
doi: 10.1016/j.anbehav.2003.04.004. |
[9] |
F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Trans. Automat. Control, 52 (2007), 852-862.
doi: 10.1109/TAC.2007.895842. |
[10] |
F. Cucker and S. Smale, Lectures on emergence, Japan J. Math., 2 (2007), 197-227.
doi: 10.1007/s11537-007-0647-x. |
[11] |
F. Cucker, S. Smale and D. Zhou, Modeling language evolution, Found. Comput. Math., 4 (2004), 315-343.
doi: 10.1007/s10208-003-0101-2. |
[12] |
F. Cucker and C. Huepe, Flocking with informed agents, Mathematics In Action, 1 (2008), 1-25.
doi: 10.5802/msia.1. |
[13] |
F. Dalmao and E. Mordecki, Cucker-Smale flocking under hierachical leadership and random interactions, SIAM J. Aappl. Math., 71 (2011), 1307-1316.
doi: 10.1137/100785910. |
[14] |
G. Grgoire, H. Chat and Y. Tu, Moving and staying together without a leader, Physica D, 181 (2003), 157-170.
doi: 10.1016/S0167-2789(03)00102-7. |
[15] |
H. Su, X. Wang and Z. Lin, Flocking of multi-agents with a virtual leader, IEEE Transactions on automatic control, 54 (2009), 293-307.
doi: 10.1109/TAC.2008.2010897. |
[16] |
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. |
[17] |
I. Couzin, J. Krause, R. James and G. Ruxton, Collective memory and spatial sorting in animal groups, J. theor. Biol., 218 (2002), 1-11.
doi: 10.1006/jtbi.2002.3065. |
[18] |
I. D. Couzin, J. Krause, R. James and G. D. Ruxton, Complex spatial group patterns result from different animal communication mechanisms, PNAS, 104 (2007), 6974-6979. |
[19] |
J. A. Carrillo, M. Fornasier, J. Rosado and G. Toscani, Asymptotic flocking dynamics for the kinetic Cuker-Smale model, SIAM J. Math. Anal., 42 (2010), 218-236.
doi: 10.1137/090757290. |
[20] |
J. Dong, Flocking under hierarchical leadership with a free-will leader, International journal of robust and nonlinear control, 23 (2013), 1891-1898. |
[21] |
J. Shen, Cucker-Smale flocking under hierarchical leadership, SIAM J. Appl. Math., 68 (2008), 694-719.
doi: 10.1137/060673254. |
[22] |
M. Agueh, R. Illner and A. Richardson, Analysis and simulations of a refined flocking and swarming model of Cuker-Smale type, Kinetic and Related Models, 4 (2011), 1-16.
doi: 10.3934/krm.2011.4.1. |
[23] |
M. Ballerini, N. Cabibbo, R. Candelier and et al., Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study, PNAS, 105 (2008), 1232-1237.
doi: 10.1073/pnas.0711437105. |
[24] |
M. Nagy, Z. Akos, D. Biro and T. Vicsek, Hierarchical group dynamics in pigeon flocks, Nature, 464 (2010), 890-894.
doi: 10.1038/nature08891. |
[25] |
S. Ha and J. 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. |
[26] |
S. 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. |
[27] |
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. |
[28] |
S. Motsch and E. Tadmor, Asymptotic flocking dynamics for the kinetic Cucker-Smale model, SIAM REVIEW, 56 (2014), 577-621.
doi: 10.1137/120901866. |
[29] |
T. Vicsek, A. Czirk, 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), 1226-1235.
doi: 10.1103/PhysRevLett.75.1226. |
[30] |
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. |
[31] |
Z. Akos, T. Vicsek and E. Kubinyi, Leadership and path characteristics during walks are linked to dominance order and individual traits in Dogs, Computational biology, 10 (2014), 1-9. |
[32] |
Z. Li and X. Xue, Cucher-Smale flocking under rooted leadership with fixed switching topologies, SIAM J. Appl. Math., 70 (2010), 3156-3174.
doi: 10.1137/100791774. |
[33] |
Z. Li and X. Xue, Cucker-Smale flocking under rooted leadership with free-will agents, Physica A, 410 (2014), 205-217.
doi: 10.1016/j.physa.2014.05.008. |
[34] |
Z. Li, Effectual leadership in flocks with hierarchy and individual preference, Discrete and Continue Dynamical Systems, 34 (2014), 3683-3702.
doi: 10.3934/dcds.2014.34.3683. |
[35] |
Z. Wang and D. Gu, A local sensor based leader-follower flocking system, in Proc. 2008 IEEE Int. Conf. Robot. Autom., (2008), 19-23. |
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