Synchronization in Complex Systems Following the Decision Based Queuing Process: The Rhythmic Applause as a Test Case

TL;DR

This paper investigates the synchronization phenomena in complex systems like rhythmic applause, using an augmented model to explain sudden synchronization and its specific timing conditions, and introduces a network formation principle.

Contribution

It extends existing models by incorporating individuality and companionship forces, explaining synchronization dynamics and proposing a network growth mechanism with power-law degree distribution.

Findings

Synchronization occurs suddenly under specific timing conditions.

A weak preferential attachment can generate complex networks with power-law degree distributions.

The model explains the timing and loss of synchronization in rhythmic applause.

Abstract

Living communities can be considered as complex systems, thus a fertile ground for studies related to their statistics and dynamics. In this study we revisit the case of the rhythmic applause by utilizing the model proposed by V\'azquez et al. [A. V\'azquez et al., Phys. Rev. E 73, 036127 (2006)] augmented with two contradicted {\it driving forces}, namely: {\it Individuality} and {\it Companionship}. To that extend, after performing computer simulations with a large number of oscillators we propose an explanation on the following open questions (a) why synchronization occurs suddenly, and b) why synchronization is observed when the clapping period ($T_c$) is $1.5 \cdot T_s < T_c < 2.0 \cdot T_s$ ($T_s$ is the mean self period of the spectators) and is lost after a time. Moreover, based on the model, a weak preferential attachment principle is proposed which can produce complex networks obeying power law in the distribution of number edges per node with exponent greater than 3.