Termination mechanisms of Turing patterns in growing systems

Gabriel Morgado, Laurence Signon, Bogdan Nowakowski, and Annie Lemarchand​

Acta Physica Polonica B (2019) Vol. 50 , No 7 


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.

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This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 711859.