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A new discrete Cucker-Smale flocking model under hierarchical leadership
1. | Department of Mathematics, National Kaohsiung Normal University, Yanchao District, Kaohsiung City 82444, Taiwan |
2. | Department of Mathematics, National Central University, Jhongli District, Taoyuan City 32001, Taiwan |
References:
[1] |
F. Cucker and J. Dong, A general collision-avoiding flocking framework, IEEE Trans. Automat. Control, 56 (2011), 1124-1129.
doi: 10.1109/TAC.2011.2107113. |
[2] |
F. Cucker and S. Smale, Best choices for regularization parameters in learning theory: On the bias-variance problem, Found. Comput. Math., 2 (2002), 413-428.
doi: 10.1007/s102080010030. |
[3] |
F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Trans. Automat. Control, 52 (2007), 852-862.
doi: 10.1109/TAC.2007.895842. |
[4] |
F. Cucker and S. Smale, On the mathematics of emergence, Jpn. J. Math., 2 (2007), 197-227.
doi: 10.1007/s11537-007-0647-x. |
[5] |
F. Dalmao and E. Moedecki, Cucker-Smale flocking under hierarchical leadership and random interactions, SIAM J. Appl. Math., 71 (2011), 1307-1316.
doi: 10.1137/100785910. |
[6] |
J. Dong, Flocking under hierarchical leadership with a free-will leader, Internat. J. Robust Nonlinear Control, 23 (2013), 1891-1898. |
[7] |
S. Ha, T. Ha and J. Kim, Emergent behavior of a Cucker-Smale type particle model with nonlinear velocity coupling, IEEE Trans. Automat. Control, 55 (2010), 1679-1683.
doi: 10.1109/TAC.2010.2046113. |
[8] |
R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
doi: 10.1017/CBO9780511840371. |
[9] |
R. A. Horn and C. R. Johnson, Matrix Analysis, second edition, Cambridge University Press, Cambridge, 2013. |
[10] |
Z. Li, Effectual leadership in flocks with hierarchy and individual preference, Discrete Contin. Dyn. Syst., 34 (2014), 3683-3702.
doi: 10.3934/dcds.2014.34.3683. |
[11] |
Z. Li and S. Ha, Cucker-Smale flocking with alternating leaders, Quart. Appl. Math., 73 (2015), 693-709.
doi: 10.1090/qam/1401. |
[12] |
Z. Li, S. Ha and X. Xue, Emergent phenomena in an ensemble of Cucker-Smale particles under joint rooted leadership, Math. Models Methods Appl. Sci., 24 (2014), 1389-1419.
doi: 10.1142/S0218202514500043. |
[13] |
Z. Li and X. Xue, Cucker-Smale flocking under rooted leadership with free-will agents, Phys. A, 410 (2014), 205-217.
doi: 10.1016/j.physa.2014.05.008. |
[14] |
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. |
[15] |
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. |
[16] |
J. Park, H. Kim and S. Ha, Cucker-Smale flocking with inter-particle bonding forces, IEEE Trans. Automat. Control, 55 (2010), 2617-2623.
doi: 10.1109/TAC.2010.2061070. |
[17] |
J. Shen, Cucker-Smale flocking under hierarchical leadership, SIAM J. Appl. Math., 68 (2007), 694-719.
doi: 10.1137/060673254. |
[18] |
Q. Song, F. Liu, J. Cao and J. Qiu, Cucker-Smale flocking with bounded cohesive and repulsive forces, Abstr. Appl. Anal., 2013, Art. ID 783279, 9 pp. |
[19] |
J. Zhou, X. Wu, W. Yu, M. Small and J. Lu, Flocking of multi-agent dynamical systems based on pseudo-leader mechanism, Systems Control Lett., 61 (2012), 195-202.
doi: 10.1016/j.sysconle.2011.10.006. |
show all references
References:
[1] |
F. Cucker and J. Dong, A general collision-avoiding flocking framework, IEEE Trans. Automat. Control, 56 (2011), 1124-1129.
doi: 10.1109/TAC.2011.2107113. |
[2] |
F. Cucker and S. Smale, Best choices for regularization parameters in learning theory: On the bias-variance problem, Found. Comput. Math., 2 (2002), 413-428.
doi: 10.1007/s102080010030. |
[3] |
F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Trans. Automat. Control, 52 (2007), 852-862.
doi: 10.1109/TAC.2007.895842. |
[4] |
F. Cucker and S. Smale, On the mathematics of emergence, Jpn. J. Math., 2 (2007), 197-227.
doi: 10.1007/s11537-007-0647-x. |
[5] |
F. Dalmao and E. Moedecki, Cucker-Smale flocking under hierarchical leadership and random interactions, SIAM J. Appl. Math., 71 (2011), 1307-1316.
doi: 10.1137/100785910. |
[6] |
J. Dong, Flocking under hierarchical leadership with a free-will leader, Internat. J. Robust Nonlinear Control, 23 (2013), 1891-1898. |
[7] |
S. Ha, T. Ha and J. Kim, Emergent behavior of a Cucker-Smale type particle model with nonlinear velocity coupling, IEEE Trans. Automat. Control, 55 (2010), 1679-1683.
doi: 10.1109/TAC.2010.2046113. |
[8] |
R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
doi: 10.1017/CBO9780511840371. |
[9] |
R. A. Horn and C. R. Johnson, Matrix Analysis, second edition, Cambridge University Press, Cambridge, 2013. |
[10] |
Z. Li, Effectual leadership in flocks with hierarchy and individual preference, Discrete Contin. Dyn. Syst., 34 (2014), 3683-3702.
doi: 10.3934/dcds.2014.34.3683. |
[11] |
Z. Li and S. Ha, Cucker-Smale flocking with alternating leaders, Quart. Appl. Math., 73 (2015), 693-709.
doi: 10.1090/qam/1401. |
[12] |
Z. Li, S. Ha and X. Xue, Emergent phenomena in an ensemble of Cucker-Smale particles under joint rooted leadership, Math. Models Methods Appl. Sci., 24 (2014), 1389-1419.
doi: 10.1142/S0218202514500043. |
[13] |
Z. Li and X. Xue, Cucker-Smale flocking under rooted leadership with free-will agents, Phys. A, 410 (2014), 205-217.
doi: 10.1016/j.physa.2014.05.008. |
[14] |
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. |
[15] |
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. |
[16] |
J. Park, H. Kim and S. Ha, Cucker-Smale flocking with inter-particle bonding forces, IEEE Trans. Automat. Control, 55 (2010), 2617-2623.
doi: 10.1109/TAC.2010.2061070. |
[17] |
J. Shen, Cucker-Smale flocking under hierarchical leadership, SIAM J. Appl. Math., 68 (2007), 694-719.
doi: 10.1137/060673254. |
[18] |
Q. Song, F. Liu, J. Cao and J. Qiu, Cucker-Smale flocking with bounded cohesive and repulsive forces, Abstr. Appl. Anal., 2013, Art. ID 783279, 9 pp. |
[19] |
J. Zhou, X. Wu, W. Yu, M. Small and J. Lu, Flocking of multi-agent dynamical systems based on pseudo-leader mechanism, Systems Control Lett., 61 (2012), 195-202.
doi: 10.1016/j.sysconle.2011.10.006. |
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