Effective reduction of a three-dimensional circadian oscillator model

TL;DR

This paper analyzes a 3D circadian oscillator model, proving the existence of a biologically meaningful attractor and simplifying it to a 2D system under certain conditions, aiding understanding of circadian dynamics.

Contribution

It introduces a reduction technique for a 3D circadian model to a 2D system on a slow manifold, enhancing analytical tractability.

Findings

Existence of a biologically relevant attractor

Reduction of the 3D system to a 2D system on a slow manifold

Simplified model retains key dynamical features

Abstract

We investigate the dynamics of a three-dimensional system modeling a molecular mechanism for the circadian rhythm in Drosophila. We first prove the existence of a compact attractor in the region with biological meaning. Under the assumption that the dimerization reactions are fast, in this attractor we reduce the three-dimensional system to a simpler two-dimensional system on the persistent normally hyperbolic slow manifold.