MEAN-FIELD LIMIT FOR PARTICLE SYSTEMS WITH TOPOLOGICAL INTERACTIONS

被引：4
作者：
Benedetto, Dario [1 ]
Caglioti, Emanuele [1 ]
Rossi, Stefano [1 ]
机构：
[1] Univ Roma La Sapienza, Dipartimento Matemat, Rome, Italy
来源：
MATHEMATICS AND MECHANICS OF COMPLEX SYSTEMS | 2021年 / 9卷 / 04期
关键词：
mean-field limit; topological interaction; Cucker-Smale model; VLASOV EQUATIONS; DYNAMICS; APPROXIMATION; PROPAGATION; BEHAVIOR; MODEL;
D O I：
10.2140/memocs.2021.9.423
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
The mean-field limit for systems of self-propelled agents with "topological interaction" cannot be obtained by means of the usual Dobrushin approach. We get results by adapting to the multidimensional case the techniques developed by Trocheris in 1986 to treat the Vlasov-Poisson equation in one dimension.
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页码：423 / 440
页数：18
相关论文
共 33 条
  • [1] [Anonymous], 1974, UNIFORM DISTRIBUTION
  • [2] Attanasi A, 2014, NAT PHYS, V10, P692, DOI [10.1038/NPHYS3035, 10.1038/nphys3035]
  • [3] Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study
    Ballerini, M.
    Calbibbo, N.
    Candeleir, R.
    Cavagna, A.
    Cisbani, E.
    Giardina, I.
    Lecomte, V.
    Orlandi, A.
    Parisi, G.
    Procaccini, A.
    Viale, M.
    Zdravkovic, V.
    [J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2008, 105 (04) : 1232 - 1237
  • [4] Some aspects of the inertial spin model for flocks and related kinetic equations
    Benedetto, D.
    Butta, P.
    Caglioti, E.
    [J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2020, 30 (10) : 1987 - 2022
  • [5] Besicovitch A. S., 1947, P CAMBRIDGE PHILOS S, V43, P590
  • [6] BESICOVITCH AS, 1946, P CAMB PHILOS SOC, V42, P1
  • [7] A GENERAL FORM OF THE COVERING PRINCIPLE AND RELATIVE DIFFERENTIATION OF ADDITIVE FUNCTIONS
    BESICOVITCH, AS
    [J]. PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1945, 41 (02): : 103 - 110
  • [8] VLASOV DYNAMICS AND ITS FLUCTUATIONS IN 1-N LIMIT OF INTERACTING CLASSICAL PARTICLES
    BRAUN, W
    HEPP, K
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1977, 56 (02) : 101 - 113
  • [9] BURKHOLDER DL, 1991, LECT NOTES MATH, V1464, P2
  • [10] A WELL-POSEDNESS THEORY IN MEASURES FOR SOME KINETIC MODELS OF COLLECTIVE MOTION
    Canizo, J. A.
    Carrillo, J. A.
    Rosado, J.
    [J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2011, 21 (03) : 515 - 539
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