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

Abstract

This paper provides an overview and critical analysis on the modeling and applications of the dynamics of human crowds, where social interactions can have an important influence on the behavioral dynamics of the crowd viewed as a living, hence complex, system. The analysis looks 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. Computational applications enlighten the role of human behaviors.2010 Mathematics Subject Classification Primary: 82D99, 91A15; Secondary: 91D10.

Particle Methods Simulations by Kinetic Theory Models of Human Crowds Accounting for Stress Conditions

“…Methods of the kinetic theory approach to model human crowds, as reviewed in [1], have been initiated in [6] for crowds in unbounded domains and further developed in [7] to account for the interactions with walls and obstacles as well as for different levels of stress, while propagation of stress by contagion has been studied in [8], [9] and [10]. Derivation of models at the macroscopic scale from the microscopic scale can be obtained by development of Hilbert type approaches [11][12][13][14].…”

“…The pioneer approach to safety problems belongs to Helbing and coworkers [15][16][17], while several developments have been recently developed as reported in the bibliography of [8]. A recent research work [18] shows how a systems approach to safety problems can be developed, where a key feature consists in accounting for the connection between local density and stress.…”

A kinetic theory approach to model pedestrian dynamics in bounded domains with obstacles

“…These artifacts can be reduced by incorporating extra rules and/or elaborate calibrations, at the price of an increased computational cost.The scale of observation for the third approach is between the previous two. Introduced in [5] and further developed in [1, 6,7,9,10,11,12], this approach derives a Boltzmann-type evolution equation for the statistical distribution function of the position and velocity of the pedestrians, in a framework close to that of the kinetic theory of gases. See also [13] for a literature review on this approach.…”

“…See also [13] for a literature review on this approach. The model proposed in [5, 6,12] is valid in unbounded domains and with a homogeneous distribution of walking ability for the pedestrians, while the extension to bounded domains is presented in [1] and further explored in [9,10,11]. In [9], more general features of behavioral-social dynamics are taken into account.…”

“…The methodology in [10] is validated by comparing the computed fundamental density-velocity diagrams with empirically observed ones and by checking that well known emerging properties are reproduced. A kinetic theory approach for modeling pedestrian dynamics in presence of social phenomena, such as the propagation of stress conditions, is presented in [11]. Finally, we refer to [7] for a thorough description of how kinetic theory and evolutionary game theory can be used to understand the dynamics of living systems.The scale of observation for the third approach is between the previous two.…”