-
Previous Article
Dispersive effects of the incompressible viscoelastic fluids
- DCDS Home
- This Issue
-
Next Article
Analysis of the attainment of boundary conditions for a nonlocal diffusive Hamilton-Jacobi equation
Collision-avoiding in the singular Cucker-Smale model with nonlinear velocity couplings
Institute of Applied and Computational Mathematics, Foundation for Research and Technology - Hellas, N. Plastira 100, Vassilika Vouton, GR - 700 13, Heraklion, Crete, Greece |
Collision avoidance is an interesting feature of the Cucker-Smale (CS) model of flocking that has been studied in many works, e.g. [
References:
[1] |
M. Agueh, R. Illner and A. Richardson,
Analysis and simulation of a refined flocking and swarming model of Cucker-Smale type, Kinet. Relat. Models, 4 (2011), 1-16.
doi: 10.3934/krm.2011.4.1. |
[2] |
S. M. Ahn, H. Choi, S.-Y. Ha and H. Lee,
On collision-avoiding initial configurations to Cucker-Smale type flocking models, Commun. Math. Sci., 10 (2012), 625-643.
doi: 10.4310/CMS.2012.v10.n2.a10. |
[3] |
J. A. Carrillo, Y.-P. Choi and M. Hauray,
Local well-posedness of the generalized Cucker-Smale model, ESAIM:Proc., 47 (2014), 17-35.
doi: 10.1051/proc/201447002. |
[4] |
J. A. Carrillo, Y.-P. Choi, P. B. Mucha and J. Peszek,
Sharp conditions to avoid collisions in singular Cucker-Smale interactions, Nonlinear Anal. Real World Appl., 37 (2017), 317-328.
doi: 10.1016/j.nonrwa.2017.02.017. |
[5] |
Y.-P. Choi and J. Haskovec,
Cucker-Smale model with normalized communication weights and time delay, Kinet. Relat. Models, 10 (2017), 1011-1033.
doi: 10.3934/krm.2017040. |
[6] |
F. Cucker and J.-G. Dong,
A general collision-avoiding flocking framework, IEEE Trans. Automat. Control, 56 (2011), 1124-1129.
doi: 10.1109/TAC.2011.2107113. |
[7] |
F. Cucker and J.-G. Dong,
A conditional, collision-avoiding, model for swarming, Discrete Contin. Dyn. Syst., 34 (2014), 1009-1020.
doi: 10.3934/dcds.2014.34.1009. |
[8] |
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. |
[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,
On the mathematics of emergence, Japan J. Math., 2 (2007), 197-227.
doi: 10.1007/s11537-007-0647-x. |
[11] |
R. Erban, J. Haskovec and Y. Sun,
A Cucker-Smale model with noise and delay, SIAM J. Appl. Math., 76 (2016), 1535-1557.
doi: 10.1137/15M1030467. |
[12] |
S.-Y. Ha, T. Ha and J.-H. Kim,
Emergent behavior of a Cucker-Smale type particle model with nonlinear velocity couplings, IEEE Trans. Automat. Control, 55 (2010), 1679-1683.
doi: 10.1109/TAC.2010.2046113. |
[13] |
S.-Y. Ha, T. Ha and J.-H. Kim, Asymptotic dynamics for the Cucker-Smale-type model with the Rayleigh friction,
J. Phys. A, 43 (2010), 315201, 19pp.
doi: 10.1088/1751-8113/43/31/315201. |
[14] |
S.-Y. Ha, K. Lee and D. Levy,
Emergence of time asymptotic flocking in a stochastic Cucker-Smale system, Commun. Math. Sci., 7 (2009), 453-469.
doi: 10.4310/CMS.2009.v7.n2.a9. |
[15] |
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. |
[16] |
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. |
[17] |
M. Hauray and P.-E. Jabin,
Particles approximations of Vlasov equations with singular forces: Propagation of chaos, Ann. Sci. Éc. Norm. Supér., 48 (2015), 891-940.
doi: 10.24033/asens.2261. |
[18] |
P.-E. Jabin,
A review of the mean field limits for Vlasov equations, Kinet. Relat. Models, 7 (2014), 661-711.
doi: 10.3934/krm.2014.7.661. |
[19] |
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. |
[20] |
P. B. Mucha and J. Peszek,
The Cucker-Smale equation: Singular communication weight, measure-valued solutions and weak-atomic uniqueness, Arch. Ration. Mech. Anal., 227 (2018), 273-308.
doi: 10.1007/s00205-017-1160-x. |
[21] |
J. Peszek,
Existence of piecewise weak solutions of a discrete Cucker-Smale's flocking model with a singular communication weight, J. Differential Equations, 257 (2014), 2900-2925.
doi: 10.1016/j.jde.2014.06.003. |
[22] |
J. Peszek,
Discrete Cucker-Smale flocking model with a weakly singular weight, SIAM J. Math. Anal., 47 (2015), 3671-3686.
doi: 10.1137/15M1009299. |
[23] |
J. Shen,
Cucker-Smale flocking under hierarchical leadership, SIAM J. Appl. Math., 68 (2007), 694-719.
doi: 10.1137/060673254. |
[24] |
T. V. Ton, N. T. H. Linh and A. Yagi,
Flocking and non-flocking behavior in a stochastic Cucker-Smale system, Anal. Appl., 12 (2014), 63-73.
doi: 10.1142/S0219530513500255. |
[25] |
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), 1226-1229.
doi: 10.1103/PhysRevLett.75.1226. |
show all references
References:
[1] |
M. Agueh, R. Illner and A. Richardson,
Analysis and simulation of a refined flocking and swarming model of Cucker-Smale type, Kinet. Relat. Models, 4 (2011), 1-16.
doi: 10.3934/krm.2011.4.1. |
[2] |
S. M. Ahn, H. Choi, S.-Y. Ha and H. Lee,
On collision-avoiding initial configurations to Cucker-Smale type flocking models, Commun. Math. Sci., 10 (2012), 625-643.
doi: 10.4310/CMS.2012.v10.n2.a10. |
[3] |
J. A. Carrillo, Y.-P. Choi and M. Hauray,
Local well-posedness of the generalized Cucker-Smale model, ESAIM:Proc., 47 (2014), 17-35.
doi: 10.1051/proc/201447002. |
[4] |
J. A. Carrillo, Y.-P. Choi, P. B. Mucha and J. Peszek,
Sharp conditions to avoid collisions in singular Cucker-Smale interactions, Nonlinear Anal. Real World Appl., 37 (2017), 317-328.
doi: 10.1016/j.nonrwa.2017.02.017. |
[5] |
Y.-P. Choi and J. Haskovec,
Cucker-Smale model with normalized communication weights and time delay, Kinet. Relat. Models, 10 (2017), 1011-1033.
doi: 10.3934/krm.2017040. |
[6] |
F. Cucker and J.-G. Dong,
A general collision-avoiding flocking framework, IEEE Trans. Automat. Control, 56 (2011), 1124-1129.
doi: 10.1109/TAC.2011.2107113. |
[7] |
F. Cucker and J.-G. Dong,
A conditional, collision-avoiding, model for swarming, Discrete Contin. Dyn. Syst., 34 (2014), 1009-1020.
doi: 10.3934/dcds.2014.34.1009. |
[8] |
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. |
[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,
On the mathematics of emergence, Japan J. Math., 2 (2007), 197-227.
doi: 10.1007/s11537-007-0647-x. |
[11] |
R. Erban, J. Haskovec and Y. Sun,
A Cucker-Smale model with noise and delay, SIAM J. Appl. Math., 76 (2016), 1535-1557.
doi: 10.1137/15M1030467. |
[12] |
S.-Y. Ha, T. Ha and J.-H. Kim,
Emergent behavior of a Cucker-Smale type particle model with nonlinear velocity couplings, IEEE Trans. Automat. Control, 55 (2010), 1679-1683.
doi: 10.1109/TAC.2010.2046113. |
[13] |
S.-Y. Ha, T. Ha and J.-H. Kim, Asymptotic dynamics for the Cucker-Smale-type model with the Rayleigh friction,
J. Phys. A, 43 (2010), 315201, 19pp.
doi: 10.1088/1751-8113/43/31/315201. |
[14] |
S.-Y. Ha, K. Lee and D. Levy,
Emergence of time asymptotic flocking in a stochastic Cucker-Smale system, Commun. Math. Sci., 7 (2009), 453-469.
doi: 10.4310/CMS.2009.v7.n2.a9. |
[15] |
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. |
[16] |
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. |
[17] |
M. Hauray and P.-E. Jabin,
Particles approximations of Vlasov equations with singular forces: Propagation of chaos, Ann. Sci. Éc. Norm. Supér., 48 (2015), 891-940.
doi: 10.24033/asens.2261. |
[18] |
P.-E. Jabin,
A review of the mean field limits for Vlasov equations, Kinet. Relat. Models, 7 (2014), 661-711.
doi: 10.3934/krm.2014.7.661. |
[19] |
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. |
[20] |
P. B. Mucha and J. Peszek,
The Cucker-Smale equation: Singular communication weight, measure-valued solutions and weak-atomic uniqueness, Arch. Ration. Mech. Anal., 227 (2018), 273-308.
doi: 10.1007/s00205-017-1160-x. |
[21] |
J. Peszek,
Existence of piecewise weak solutions of a discrete Cucker-Smale's flocking model with a singular communication weight, J. Differential Equations, 257 (2014), 2900-2925.
doi: 10.1016/j.jde.2014.06.003. |
[22] |
J. Peszek,
Discrete Cucker-Smale flocking model with a weakly singular weight, SIAM J. Math. Anal., 47 (2015), 3671-3686.
doi: 10.1137/15M1009299. |
[23] |
J. Shen,
Cucker-Smale flocking under hierarchical leadership, SIAM J. Appl. Math., 68 (2007), 694-719.
doi: 10.1137/060673254. |
[24] |
T. V. Ton, N. T. H. Linh and A. Yagi,
Flocking and non-flocking behavior in a stochastic Cucker-Smale system, Anal. Appl., 12 (2014), 63-73.
doi: 10.1142/S0219530513500255. |
[25] |
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), 1226-1229.
doi: 10.1103/PhysRevLett.75.1226. |
[1] |
Seung-Yeal Ha, Dongnam Ko, Yinglong Zhang, Xiongtao Zhang. Emergent dynamics in the interactions of Cucker-Smale ensembles. Kinetic and Related Models, 2017, 10 (3) : 689-723. doi: 10.3934/krm.2017028 |
[2] |
Seung-Yeal Ha, Jeongho Kim, Peter Pickl, Xiongtao Zhang. A probabilistic approach for the mean-field limit to the Cucker-Smale model with a singular communication. Kinetic and Related Models, 2019, 12 (5) : 1045-1067. doi: 10.3934/krm.2019039 |
[3] |
Young-Pil Choi, Seung-Yeal Ha, Jeongho Kim. Propagation of regularity and finite-time collisions for the thermomechanical Cucker-Smale model with a singular communication. Networks and Heterogeneous Media, 2018, 13 (3) : 379-407. doi: 10.3934/nhm.2018017 |
[4] |
Young-Pil Choi, Cristina Pignotti. Emergent behavior of Cucker-Smale model with normalized weights and distributed time delays. Networks and Heterogeneous Media, 2019, 14 (4) : 789-804. doi: 10.3934/nhm.2019032 |
[5] |
Young-Pil Choi, Jan Haskovec. Cucker-Smale model with normalized communication weights and time delay. Kinetic and Related Models, 2017, 10 (4) : 1011-1033. doi: 10.3934/krm.2017040 |
[6] |
Zili Chen, Xiuxia Yin. The delayed Cucker-Smale model with short range communication weights. Kinetic and Related Models, 2021, 14 (6) : 929-948. doi: 10.3934/krm.2021030 |
[7] |
Hyunjin Ahn, Seung-Yeal Ha, Woojoo Shim. Emergent dynamics of a thermodynamic Cucker-Smale ensemble on complete Riemannian manifolds. Kinetic and Related Models, 2021, 14 (2) : 323-351. doi: 10.3934/krm.2021007 |
[8] |
Jianfei Cheng, Xiao Wang, Yicheng Liu. Collision-avoidance and flocking in the Cucker–Smale-type model with a discontinuous controller. Discrete and Continuous Dynamical Systems - S, 2022, 15 (7) : 1733-1748. doi: 10.3934/dcdss.2021169 |
[9] |
Jinwook Jung, Peter Kuchling. Emergent dynamics of the fractional Cucker-Smale model under general network topologies. Communications on Pure and Applied Analysis, 2022, 21 (8) : 2831-2856. doi: 10.3934/cpaa.2022077 |
[10] |
Linglong Du, Xinyun Zhou. The stochastic delayed Cucker-Smale system in a harmonic potential field. Kinetic and Related Models, , () : -. doi: 10.3934/krm.2022022 |
[11] |
Lining Ru, Xiaoping Xue. Flocking of Cucker-Smale model with intrinsic dynamics. Discrete and Continuous Dynamical Systems - B, 2019, 24 (12) : 6817-6835. doi: 10.3934/dcdsb.2019168 |
[12] |
Mauro Rodriguez Cartabia. Cucker-Smale model with time delay. Discrete and Continuous Dynamical Systems, 2022, 42 (5) : 2409-2432. doi: 10.3934/dcds.2021195 |
[13] |
Roberto Natalini, Thierry Paul. On the mean field limit for Cucker-Smale models. Discrete and Continuous Dynamical Systems - B, 2022, 27 (5) : 2873-2889. doi: 10.3934/dcdsb.2021164 |
[14] |
Hyunjin Ahn. Uniform stability of the Cucker–Smale and thermodynamic Cucker–Smale ensembles with singular kernels. Networks and Heterogeneous Media, 2022 doi: 10.3934/nhm.2022025 |
[15] |
Helmut Maurer, Tanya Tarnopolskaya, Neale Fulton. Computation of bang-bang and singular controls in collision avoidance. Journal of Industrial and Management Optimization, 2014, 10 (2) : 443-460. doi: 10.3934/jimo.2014.10.443 |
[16] |
Seung-Yeal Ha, Shi Jin. Local sensitivity analysis for the Cucker-Smale model with random inputs. Kinetic and Related Models, 2018, 11 (4) : 859-889. doi: 10.3934/krm.2018034 |
[17] |
Martial Agueh, Reinhard Illner, Ashlin Richardson. Analysis and simulations of a refined flocking and swarming model of Cucker-Smale type. Kinetic and Related Models, 2011, 4 (1) : 1-16. doi: 10.3934/krm.2011.4.1 |
[18] |
Marco Caponigro, Massimo Fornasier, Benedetto Piccoli, Emmanuel Trélat. Sparse stabilization and optimal control of the Cucker-Smale model. Mathematical Control and Related Fields, 2013, 3 (4) : 447-466. doi: 10.3934/mcrf.2013.3.447 |
[19] |
Martin Friesen, Oleksandr Kutoviy. Stochastic Cucker-Smale flocking dynamics of jump-type. Kinetic and Related Models, 2020, 13 (2) : 211-247. doi: 10.3934/krm.2020008 |
[20] |
Seung-Yeal Ha, Dohyun Kim, Jinyeong Park. Fast and slow velocity alignments in a Cucker-Smale ensemble with adaptive couplings. Communications on Pure and Applied Analysis, 2020, 19 (9) : 4621-4654. doi: 10.3934/cpaa.2020209 |
2021 Impact Factor: 1.588
Tools
Metrics
Other articles
by authors
[Back to Top]