Termination Mechanisms of Turing Patterns in Growing Systems

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Authors
Morgado, Gabriel
Nowakowski, Bogdan
Lemarchand, Annie
Date
2019-04-24
Journal Title
Journal ISSN
Volume Title
Publisher
Jagiellonian University, Polish Academy of Art and Sciences
License
Creative Commons License
Creative Commons Attribution 4.0 International License
Abstract
The question of the termination of a periodic spatial structure of Turingtype 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.
Description
Keywords
nonlinear sciences    pattern formation and solitons
Citation
Morgado, Gabriel & Signon, Laurence & Nowakowski, B. & Lemarchand, Annie. (2019). Termination Mechanisms of Turing Patterns in Growing Systems. Acta Physica Polonica B. 50. 1369. 10.5506/APhysPolB.50.1369.
URI
https://open.icm.edu.pl/handle/123456789/21146
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Artykuły ICHF PAN / IPC PAS Articles