Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.07275 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We study a two-variable dynamical system modeling pH oscillations in the urea-urease reaction within giant lipid vesicles -- a problem that intrinsically contains multiple, well-separated timescales. Building on an existing, deterministic formulation via ordinary differential equations, we resolve different orders of magnitude within a small parameter and analyze the system's limit cycle behavior using geometric singular perturbation theory (GSPT). By introducing two different coordinate scalings -- each valid in a distinct region of the phase space -- we resolve the local dynamics near critical fold points, using the extension of GSPT through such singular points due to Krupa and Szmolyan. This framework enables a geometric decomposition of the periodic orbits into slow and fast segments and yields closed-form estimates for the period of oscillation. In particular, we link the existence of such oscillations to an underlying biochemical asymmetry, namely, the differential transport across the vesicle membrane.