A periodic model for the dynamics of cell volume

TL;DR

This paper proves the existence, uniqueness, and global stability of positive periodic solutions in a cell volume flux model, confirming previous conjectures and advancing understanding of cell volume dynamics.

Contribution

It establishes the first rigorous proof of positive periodic solutions and their global attractor properties in the cell volume flux model.

Findings

Existence and uniqueness of positive periodic solutions

Periodic solutions act as global attractors

Results confirm previous conjectures in the field

Abstract

We prove the existence and uniqueness of positive periodic solution for a model describing the dynamics of cell volume flux, introduced in Julio A. Hernandez \cite{H}. We also show that the periodic solution is a global attractor. Our results confirm the conjectures made in an interesting recent book of P.J. Torres \cite{T}.