Modified Kuramoto model with inverse-square law coupling and spatial time delay

We propose a modified Kuramoto model to describe the hand-clapping synchronization observed in a large group of people. There are two different ingredients in our model: The finiteness of the sound speed leads to the time-delay effect across the system, and the large distance makes the sound intensity decrease significantly. These two different but related factors are expected to make the synchrony in a large audience hard to achieve. We numerically and analytically test which between the two factors can be crucial to explain the failure of hand-clapping synchronization in a large group of people. We conclude that the time-delay effect due to the finite sound speed is not as important as the effect of the decreasing sound intensity with distance as long as the audience size is not too big. (C) 2021 Elsevier B.V. All rights reserved.