Díaz Díaz, Jesús Ildefonso
(2007)
*A variant of the Smale's model for flocks formation.*
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A: Matemáticas , 101
(2).
pp. 225-228.
ISSN 1578-7303

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## Abstract

Motivated by a recent lecture of S. Smale, we propose here a variant of the model considered by F. Cucker and S. Smale for the formation of uniform flocks allowing to prove that the formation of an uniform structure take place in a finite time (and not merely when t converges to infinity).

Item Type: | Article |
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Uncontrolled Keywords: | flocks, finite time convergence to equilibrium, nonlinear ordinary differential systems |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 15293 |

References: | Antontsev, S. N., Díaz, J. I. and Shmarev, S. I., (2002). Energy Methods for Free Boundary Problems: Applications to Non-linear PDEs and Fluid Mechanics, Bikhäuser, Boston, Progress in Nonlinear Differential Equations and Their Applications, 48. Cucker, F. and Smale, S., (2007). Emergent behavior in Flock, IEEE Transactions on automatic control, 52, 5, 852–862. Cucker, F., Smale, S. and Zhou, D.-X., (2004). Modeling language evolution, Found. Comput. Math., 4, 315–343. Díaz, J. I. Energy methods for free boundary problems: new results and some remarks on numerical algorithms, Serie electronique de la SMAI, Esaim Proc. Flierl, G., Grünbaum, D., Levin, S. and Olson, D., (1999). From individuals to aggregations: the interplay between behavior and physics, J. Theor. Biol., 196, 397–454. Ke, J., Minett, J., Au, C.-P. and Wang, W.S.-Y., (2002). Self-organization and selection in the emergence of vocabulary, Complexity, 7, 41–54. Smale, S. (2007). The changing directions of Mathematics, Lecture at the International Symposium "The frontiers of Mathematics", Fundación Ramón Areces, Madrid, June 7–8, 2007. Organized by the CSIC and the RAC. Vicsek, T., Czirók, A., Ben-Jacob, E. and Shochet., O., (1995). Novel type of phase transition in a system of self-driven particles, Phys. Rev. Letters, 75, 1226–1229. |

Deposited On: | 21 May 2012 09:45 |

Last Modified: | 06 Feb 2014 10:21 |

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