Flocking in noisy environments

Journal des Mathematiques Pures et Appliquees

Volumn 89, Issue 3, 2008, Pages 278-296

  Cucker, Felipe ^a   Mordecki, Ernesto ^b  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSIDAD DE LA REPÚBLICA   (Uruguay)

Author keywords

Consensus; Emergent behavior; Flocking

Indexed keywords

EID: 39849084055     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2007.12.002     Document Type: Article

References (27)

1. Adler R.J. An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes (1990), IMS, Hayward, CA
2. Arnold S.F. Mathematical Statistics (1990), Prentice Hall, Englewood Cliffs, N.J.
3. J.M. Azaïs, M. Wschebor, Level Sets and Extrema of Random Processes and Fields, book in preparation
4. Billingsley P. Probability and Measure. Wiley Series in Probability and Mathematical Statistics. third ed. (1995), John Wiley & Sons Inc., New York A Wiley-Interscience Publication
5. Buhl J., Sumpter D.J.T., Couzin I.D., Hale J.J., Despland E., Miller E.R., and Simpson S.J. From disorder to order in marching locusts. Science 312 (2006) 1402-1406
6. Y.L. Chuang, Y.R. Huang, M.R. D'Orsogna, A.L. Bertozzi, Multi-vehicle flocking: Scalability of cooperative control algorithms using pairwise potentials, preprint, 2006
7. Cramér H., and Leadbetter M.R. Stationary and Related Stochastic Processes (2004), Dover reprint
8. Cucker F., and Smale S. Best choices for regularization parameters in learning theory. Found. Comput. Math. 2 (2002) 413-428
9. Cucker F., and Smale S. Emergent behavior in flocks. IEEE Trans. on Autom. Control 52 (2007) 852-862
10. Cucker F., and Smale S. On the mathematics of emergence. Japan J. Math. 2 (2007) 197-227
11. Cucker F., Smale S., and Zhou D.X. Modeling language evolution. Found. Comput. Math. 4 (2004) 315-343
12. Davies R.B. Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 64 (1977) 247-254
13. Flierl G., Grünbaum D., Levin S., and Olson D. From individuals to aggregations: the interplay between behavior and physics. J. Theor. Biol. 196 (1999) 397-454
14. Higham N. Accuracy and Stability of Numerical Algorithms (1996), SIAM
15. Hirsch M., and Smale S. Differential Equations, Dynamical Systems, and Linear Algebra. Pure and Applied Mathematics vol. 60 (1974), Academic Press
16. Itô K. Essentials of Stochastic Processes. Translations of Mathematical Monographs vol. 231 (2006), AMS, Providence, RI Translated from the 1957 Japanese original by Yuji Ito
17. Jadbabaie A., Lin J., and Morse A.S. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. on Autom. Control 48 (2003) 988-1001
18. Ke J., Minett J., Au C.-P., and Wang W.S.-Y. Self-organization and selection in the emergence of vocabulary. Complexity 7 (2002) 41-54
19. Kurtz T.G., and Protter P. Weak limit theorems for stochastic integrals and stochastic differential equations. Ann. Probab. 19 (1991) 1035-1070
20. Niyogi P. The Computational Nature of Language Learning and Evolution (2006), The MIT Press
21. Oksendal B. Stochastic Differential Equations. sixth ed. Universitext (2003), Springer-Verlag, Berlin
22. Shen J. Cucker-Smale flocking under hierarchical leadership. preprint, available at (2007). http://www.math.umn.edu/~jhshen
23. H.G. Tanner, A. Jadbabaie, G.J. Pappas, Stable flocking of mobile agents, Part I: Fixed topology, and Part II: Dynamic topology, in: Proceedings of the 42nd IEEE Conference on Decision and Control, 2003, pp. 2010-2021
24. Topaz C.M., Bertozzi A.L., and Lewis M.A. A nonlocal continuum model for biological aggregation. Bulletin of Mathematical Biology 68 (2006) 1601-1623
25. J.N. Tsitsiklis, Problems in decentralized decision making and computation, PhD thesis, Department of EECS, MIT, 1984
26. Tsitsiklis J.N., Bertsekas D.P., and Athans M. Distributed asynchronous deterministic and stochastic gradient optimization algorithms. IEEE Trans. on Autom. Control 31 (1986) 803-812
27. Vicsek T., Czirók A., Ben-Jacob E., and Shochet O. Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75 (1995) 1226-1229