# Temporal oscillations in Becker-Doering equations with atomization

## TL;DR

This paper demonstrates that a modified Becker-Doering coagulation-fragmentation system with atomization exhibits time-periodic solutions arising from Hopf bifurcation, modeling oscillatory behavior in physical chemistry gas evolution processes.

## Contribution

It introduces a novel variant of the Becker-Doering equations incorporating atomization and proves the existence of oscillatory solutions via bifurcation analysis.

## Key findings

- Time-periodic solutions are proven to exist.
- Oscillations arise through Hopf bifurcation.
- Model captures physical chemistry gas evolution oscillations.

## Abstract

We prove that time-periodic solutions arise via Hopf bifurcation in a finite closed system of coagulation-fragmentation equations. The system we treat is a variant of the Becker-Doering equations, in which clusters grow or shrink by addition or deletion of monomers. To this is added a linear atomization reaction for clusters of maximum size. The structure of the system is motivated by models of gas evolution oscillators in physical chemistry, which exhibit temporal oscillations under certain input/output conditions.