Special Issue on Traffic, Crowd, and SwarmsNo Access

ON THE MODELLING CROWD DYNAMICS FROM SCALING TO HYPERBOLIC MACROSCOPIC MODELS

NICOLA BELLOMO

Department of Mathematics, Politecnico, Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

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and

CHRISTIAN DOGBÉ

Department of Mathematics, University of Caen, CNRS UMR 6139 BP 5186, F-14032 Caen, France

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https://doi.org/10.1142/S0218202508003054Cited by:147 (Source: Crossref)

Abstract

This paper, that deals with the modelling of crowd dynamics, is the first one of a project finalized to develop a mathematical theory refereing to the modelling of the complex systems constituted by several interacting individuals in bounded and unbounded domains. The first part of the paper is devoted to scaling and related representation problems, then the macroscopic scale is selected and a variety of models are proposed according to different approximations of the pedestrian strategies and interactions. The second part of the paper deals with a qualitative analysis of the models with the aim of analyzing their properties. Finally, a critical analysis is proposed in view of further development of the modelling approach. Additional reasonings are devoted to understanding the conceptual differences between crowd and swarm modelling.

Keywords:

AMSC: 91D10, 92D25, 90B20

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