Mass conservative reaction diffusion systems describing cell polarity

TL;DR

This paper analyzes a mass-conservative reaction-diffusion system modeling cell polarity, identifying parameter ranges where solutions stabilize exponentially to homogeneous equilibria, including constant and spatially uniform orbits.

Contribution

It provides a rigorous analysis of the stability and long-term behavior of a reaction-diffusion model for cell polarity, highlighting conditions for exponential convergence.

Findings

Solutions converge exponentially to homogeneous equilibria.

The $\omega$-limit set includes constant solutions and homogeneous orbits.

Parameter ranges for stability are characterized.

Abstract

A reaction-diffusion system with mass conservation modelling cell polarity is considered. A range of the parameters is found where the solution converges exponentially to the constant equilibrium and the $\omega$-limit set of the solution is spatially homogeneous, containing the constant stationary solution as well as possible spatially homogeneous orbits.