Dynamic Transitions and Stability for the Acetabularia Whorl Formation

TL;DR

This paper analyzes how calcium concentration influences Acetabularia whorl formation using a reaction-diffusion model, identifying various types of dynamical transitions through theoretical and numerical methods.

Contribution

It applies Ma & Wang's dynamical transition theory to a biological pattern formation model, revealing multiple transition types under different conditions.

Findings

All three transition types—continuous, catastrophic, and random—can occur.

Linear analysis and numerical simulations support the transition classifications.

The study advances understanding of pattern formation dynamics in biological systems.

Abstract

Dynamical transitions of the Acetabularia whorl formation caused by outside calcium concentration is carefully analyzed using a chemical reaction diffusion model on a thin annulus. Restricting ourselves with Turing instabilities, we found all three types of transition, continuous, catastrophic and random can occur under different parameter regimes. Detailed linear analysis and numerical investigations are also provided. The main tool used in the transition analysis is Ma \& Wang's dynamical transition theory including the center manifold reduction.