# American Institute of Mathematical Sciences

• Previous Article
Emergence of aggregation in the swarm sphere model with adaptive coupling laws
• KRM Home
• This Issue
• Next Article
A global existence of classical solutions to the two-dimensional Vlasov-Fokker-Planck and magnetohydrodynamics equations with large initial data
April  2019, 12(2): 397-409. doi: 10.3934/krm.2019017

## On the interplay between behavioral dynamics and social interactions in human crowds

 (1). Politecnico of Torino and Collegio Carlo Alberto, Torino, Italy (2). School of Engineering, University of Edinburgh, Edinburgh, United Kingdom (3). Mathematics and Population Dynamics Laboratory-UMMISCO, Faculty of Sciences of Semlalia of Marrakech, Cadi Ayyad Univ., Morocco (4). Jacques Louis-Lions Laboratory, Pierre et Marie Curie University, Paris 6, France

Received  May 2018 Published  November 2018

This paper presents a computational modeling approach to the dynamics of human crowds, where social interactions can have an important influence on the behavioral dynamics of pedestrians. The modeling of the contagion and propagation of emotional states is carried out by looking at real physical situations where safety problems might arise in some specific circumstances. The approach is based on the methods of the kinetic theory of active particles. The evacuation of a metro station is simulated to enlighten the role of the emotional state in the overall dynamics.

Citation: Nicola Bellomo, Livio Gibelli, Nisrine Outada. On the interplay between behavioral dynamics and social interactions in human crowds. Kinetic & Related Models, 2019, 12 (2) : 397-409. doi: 10.3934/krm.2019017
##### References:

show all references

##### References:
Geometry of the venue
Density contour plots of the mean density of the emotional state, $\rho \bar{u}$, with (pedestrians on the left) and without (pedestrians on the right) social interactions at different times
Density contour plots of the mean density of the emotional state, $\rho \bar{u}$, with (pedestrians on the left) and without (pedestrians on the right) social interactions at different times
Averaged value of the emotional state of the crowd, $\bar{U}$, versus time for different values of the social parameter
 [1] Daewa Kim, Annalisa Quaini. A kinetic theory approach to model pedestrian dynamics in bounded domains with obstacles. Kinetic & Related Models, 2019, 12 (6) : 1273-1296. doi: 10.3934/krm.2019049 [2] Nicola Bellomo, Abdelghani Bellouquid. On the modeling of crowd dynamics: Looking at the beautiful shapes of swarms. Networks & Heterogeneous Media, 2011, 6 (3) : 383-399. doi: 10.3934/nhm.2011.6.383 [3] Nicola Bellomo, Miguel A. Herrero, Andrea Tosin. On the dynamics of social conflicts: Looking for the black swan. Kinetic & Related Models, 2013, 6 (3) : 459-479. doi: 10.3934/krm.2013.6.459 [4] Robin Cohen, Alan Tsang, Krishna Vaidyanathan, Haotian Zhang. Analyzing opinion dynamics in online social networks. Big Data & Information Analytics, 2016, 1 (4) : 279-298. doi: 10.3934/bdia.2016011 [5] Pierre Degond, Gadi Fibich, Benedetto Piccoli, Eitan Tadmor. Special issue on modeling and control in social dynamics. Networks & Heterogeneous Media, 2015, 10 (3) : i-ii. doi: 10.3934/nhm.2015.10.3i [6] Veronika Schleper. A hybrid model for traffic flow and crowd dynamics with random individual properties. Mathematical Biosciences & Engineering, 2015, 12 (2) : 393-413. doi: 10.3934/mbe.2015.12.393 [7] Sebastien Motsch, Mehdi Moussaïd, Elsa G. Guillot, Mathieu Moreau, Julien Pettré, Guy Theraulaz, Cécile Appert-Rolland, Pierre Degond. Modeling crowd dynamics through coarse-grained data analysis. Mathematical Biosciences & Engineering, 2018, 15 (6) : 1271-1290. doi: 10.3934/mbe.2018059 [8] Clinton Innes, Razvan C. Fetecau, Ralf W. Wittenberg. Modelling heterogeneity and an open-mindedness social norm in opinion dynamics. Networks & Heterogeneous Media, 2017, 12 (1) : 59-92. doi: 10.3934/nhm.2017003 [9] Alessandro Corbetta, Adrian Muntean, Kiamars Vafayi. Parameter estimation of social forces in pedestrian dynamics models via a probabilistic method. Mathematical Biosciences & Engineering, 2015, 12 (2) : 337-356. doi: 10.3934/mbe.2015.12.337 [10] Martha G. Alatriste-Contreras, Juan Gabriel Brida, Martin Puchet Anyul. Structural change and economic dynamics: Rethinking from the complexity approach. Journal of Dynamics & Games, 2019, 6 (2) : 87-106. doi: 10.3934/jdg.2019007 [11] Simone Farinelli. Geometric arbitrage theory and market dynamics. Journal of Geometric Mechanics, 2015, 7 (4) : 431-471. doi: 10.3934/jgm.2015.7.431 [12] Mirosław Lachowicz, Andrea Quartarone, Tatiana V. Ryabukha. Stability of solutions of kinetic equations corresponding to the replicator dynamics. Kinetic & Related Models, 2014, 7 (1) : 109-119. doi: 10.3934/krm.2014.7.109 [13] Philippe Pécol, Pierre Argoul, Stefano Dal Pont, Silvano Erlicher. The non-smooth view for contact dynamics by Michel Frémond extended to the modeling of crowd movements. Discrete & Continuous Dynamical Systems - S, 2013, 6 (2) : 547-565. doi: 10.3934/dcdss.2013.6.547 [14] Tuan Hiep Pham, Jérôme Laverne, Jean-Jacques Marigo. Stress gradient effects on the nucleation and propagation of cohesive cracks. Discrete & Continuous Dynamical Systems - S, 2016, 9 (2) : 557-584. doi: 10.3934/dcdss.2016012 [15] Pablo Álvarez-Caudevilla, Julián López-Gómez. The dynamics of a class of cooperative systems. Discrete & Continuous Dynamical Systems - A, 2010, 26 (2) : 397-415. doi: 10.3934/dcds.2010.26.397 [16] Michael Hochman. Lectures on dynamics, fractal geometry, and metric number theory. Journal of Modern Dynamics, 2014, 8 (3&4) : 437-497. doi: 10.3934/jmd.2014.8.437 [17] Antonio Ambrosetti, Massimiliano Berti. Applications of critical point theory to homoclinics and complex dynamics. Conference Publications, 1998, 1998 (Special) : 72-78. doi: 10.3934/proc.1998.1998.72 [18] M. D. König, Stefano Battiston, M. Napoletano, F. Schweitzer. On algebraic graph theory and the dynamics of innovation networks. Networks & Heterogeneous Media, 2008, 3 (2) : 201-219. doi: 10.3934/nhm.2008.3.201 [19] Giacomo Albi, Lorenzo Pareschi, Mattia Zanella. Opinion dynamics over complex networks: Kinetic modelling and numerical methods. Kinetic & Related Models, 2017, 10 (1) : 1-32. doi: 10.3934/krm.2017001 [20] Carlota M. Cuesta, Sabine Hittmeir, Christian Schmeiser. Weak shocks of a BGK kinetic model for isentropic gas dynamics. Kinetic & Related Models, 2010, 3 (2) : 255-279. doi: 10.3934/krm.2010.3.255

2018 Impact Factor: 1.38