A model of synchronisation in crowd dynamics

Abstract

• A new model for crowd synchronisation is suggested. • The model is deterministic and involves Hill-type equations for double pendulums. • A suitable function measuring the synchronisation between individuals is defined. • Numerical experiments show a good matching between real crowds and our model. This study is motivated by the lack of adequate models of dynamic loading of civil engineering structures that are primarily occupied by active groups and crowds of people, such as footbridges, floors and grandstands. The primary objective is to develop a mathematical model of synchronisation of multiple people performing cyclic motion such as walking, running, jumping and bouncing. In conjunction with a quality model of individual loading, the sync model is the key ingredient needed to provide a reliable numerical generator of aggregate dynamic excitation of the supporting structure. The model describes the effect of periodic external cues on the crowd motion, such as perceptible vibration of the ground and a music beat, and the mutual interaction between individuals. The main feature of the model is that it is linear and deterministic , no randomness and no nonlinearity for the sake of simplicity and efficiency: it is inspired to models of coupled pendulums and the governing equations feature Mathieu-type behaviours. The modelling parameters have a physical interpretation and their values can be calibrated to potentially match experimental measurements.