Steady-state dynamics of an audience applause model
Abstract
We propose a compartmental model for the dynamics of audience applause consisting of agents that are either silent (S) or clapping (C). The model includes two mechanisms. The first is a feedback mechanism that is parametrized by α which enhances the probability a that agents in state C influence those in state S to transition to C. Parameters α and a are simplified to ā, where ā = aα. The second is a modulating mechanism that is parametrized by β which limits the probability b that those in state C transition to S. The steady-state dynamics of the resulting equations show that three possible solutions can exist, which includes a trivial case when all agents rest at S. Since negative steady-state values are extraneous solutions, only two of these solutions exist for ā greater than a critical parameter value ā1. For β > 1, we find a second critical parameter value ā2 such that a second non-trivial non-extraneous but unstable solution exists. We confirm our results by agent-based Monte Carlo simulations.
By submitting their manuscript to the Samahang Pisika ng Pilipinas (SPP) for consideration, the Authors warrant that their work is original, does not infringe on existing copyrights, and is not under active consideration for publication elsewhere.
Upon acceptance of their manuscript, the Authors further agree to grant SPP the non-exclusive, worldwide, and royalty-free rights to record, edit, copy, reproduce, publish, distribute, and use all or part of the manuscript for any purpose, in any media now existing or developed in the future, either individually or as part of a collection.
All other associated economic and moral rights as granted by the Intellectual Property Code of the Philippines are maintained by the Authors.
