Model of coordinated crowd dynamics

This paper presents a mathematical model of synchronisation of multiple people during cyclic activities such as walking, running, jumping and bouncing. Providing that quality models of individual loading for these activities do exist, the sync model is the key component towards an urgently needed yet reliable model of artificial dynamic loading due to multiple active occupants. A model proposed here describes the effect of external and internal factors on the crowd dynamics. The former includes periodic external stimuli on the body motion of individuals, such as perceptible vibration of the ground and music beats. The later addresses the mutual interaction between individuals, such as possibility to see, hear or touch each other. Modelling approach is inspired by the existing models of coupled pendulums while the governing equations feature Mathieu-type behaviour. For the sake of simplicity and efficiency, the model is kept linear and deterministic. All modelling parameters have a physical interpretation and their values can be calibrated to match experimental measurements.