# Terminaison mechanisms of Turing patterns in growing systems

## TL;DR

This paper investigates how Turing patterns in growing systems can naturally terminate through parameter changes, combining analytical and numerical methods to propose a controllable mechanism for pattern cessation.

## Contribution

It introduces a novel mechanism for Turing pattern termination based on local concentration increases, supported by analytical stability analysis and numerical validation.

## Key findings

- A local increase in reservoir concentration can stop Turing patterns.
- Analytical conditions for pattern termination are derived.
- Numerical simulations confirm the proposed termination mechanism.

## Abstract

The question of the termination of a periodic spatial structure of Turing type in a growing system is addressed in a chemical engineering perspective and a biomimetic approach. The effects of the dynamical parameters on the stability and the wavelength of the structure are analytically studied and used to propose experimental conditions for which a Turing pattern stops by itself with a decreasing wavelength. The proposed mechanism is successfully checked by the numerical integration of the equations governing the dynamics of the activator and the inhibitor. We conclude that a local increase of the concentration of the reservoir which controls the injection rate of the inhibitor into the system can be used to achieve the appropriate termination of a Turing pattern.