Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2603.01177

Geometric singular perturbation analysis of the active metabolic oscillator in pancreatic \b{eta}-cells

Prannath Moolchand·Martin Wechselberger
View original source ↗Read source document ↗Export metadata ↓

Abstract

Pancreatic \b{eta}-cells secrete insulin in response to blood sugar levels to maintain glucose homeostasis. This vital insulin exocytosis is controlled by the cell's bursting behaviours, which are regulated by tight bidirectional coupling of inherent electrical and metabolic oscillators. The Integrated Oscillator Model suggests that slower metabolic oscillations are mediated either by glycolytic oscillations-through an independent active metabolic oscillator (AMO)-or by Ca2+ effects on ATP consumption via a passive metabolic oscillator (PMO). By clamping the Ca2+ and ATP dynamics, our study focuses on the decoupled AMO which is the driver of pulsatile dynamics. Using appropriate reference scales, we first non-dimensionalise the model to identify small parameters and processes evolving on different timescales. We show that the AMO can be recast as a surrogate relaxation oscillator, a more general class of multiple timescale problems involving oscillation cycles comprising fast and slow segments, which are amenable to rigorous analysis using the machinery of geometric singular perturbation theory. Using the parametrisation method to identify invariant manifolds and blow-up analysis to desingularise degenerate vector fields, we fully characterise the hierarchy of timescales and the complex singular geometry constituting the metabolic oscillations. Our work considerably extends the `fast-slow' analysis of glycolytic oscillators and is a stepping stone towards understanding how the slower metabolic system temporally patterns the faster electrical bursting dynamics.

Explore related subjects

math.DS

Keep this discovery

BibTeXRIS

Prannath Moolchand, Martin Wechselberger. 2026-03-01. Geometric singular perturbation analysis of the active metabolic oscillator in pancreatic \b{eta}-cells. https://arxiv.org/abs/2603.01177

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Admissible Fourier Lengths, KAM Reducibility, and Spectral Applications

We develop a perturbative KAM reducibility theory for one-frequency $\mathrm{SL}(2,\mathbb{R})$ cocycles based on an admissible Fourier length $\ell$. The regularity relevant to the iteration is measured by positive adapted Fourier width rather than ordinary smoothness in the Euclidean length $|n|$. The same length governs Fourier decay, truncation and resonance scales, and the arithmetic condition controlling the small divisors. This framework contains the classical analytic and Gevrey settings, while non-monotone choices of $\ell$ allow classical nowhere differentiable Weierstrass-type perturbations and continuous perturbations outside every positive H\"older class. As spectral applications, we obtain purely absolutely continuous spectrum for every phase and $1/2$-H\"older continuity of the integrated density of states for the associated quasiperiodic Schr\"odinger operators. The Aubry dual has pure point spectrum for Lebesgue almost every dual phase, with eigenfunctions exponentially localized in the metric induced by $\ell$. We also construct nowhere differentiable quasiperiodic potentials with purely absolutely continuous Cantor spectrum.

math.DS↗
arXiv2026

Dynamics inside the attracting basins of some skew products

Polynomial skew products in $\mathbb{C}^2$ are maps of the form $F(z,w)=(P(z),Q(z,w))$, where $P$ and $Q$ are polynomials. Their local dynamics have been widely investigated. In this paper, we study the global dynamics inside Fatou components of some skew products. We consider all the inverse images in a Fatou component of a given point and use the Kobayashi metric to measure the distance between points. In the cases we consider, there are always arbitrarily large Kobayashi balls in the complement of these inverse sets.

math.DS↗
arXiv2026

Ergodicity of dynamical systems without uniqueness of orbits

Recently, there has been considerable interest in the study of non-deterministic dynamical systems. To analyze the chaotic behavior of such systems from a measure-theoretic viewpoint, it is desirable to consider ergodicity. However, the classical definition of ergodicity involves invariant sets, whose definition is not unique for non-deterministic dynamical systems. Thus, we are led to the question of which invariance yields an interesting definition of ergodicity. Here, we propose a definition based on the strong backward invariance and show that analogs of classical results hold. We also consider implications of the Birkhoff ergodic theorem for systems without uniqueness of orbits.

math.DS↗