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arXiv · 2412.13783

Minimum nonlinearity for pattern-forming Turing instability in a mathematical autocatalytic model

Javier López-Pedrares·Marcos Suárez-Vázquez·Juan Pérez-Mercader·Alberto P. Muñuzuri
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Abstract

Pattern formation is ubiquitous in nature and the mechanism widely-accepted to underlay them is based on the Turing instability, predicted by Alan Turing decades ago. This is a non-trivial mechanism that involves nonlinear interaction terms between the different species involved and transport mechanisms. We present here a mathematical analysis aiming to explore the mathematical constraints that a reaction-diffusion dynamical model should comply in order to exhibit a Turing instability. The main conclusion limits the existence of this instability to nonlinearity degrees larger or equal to three.

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Javier López-Pedrares, Marcos Suárez-Vázquez, Juan Pérez-Mercader, Alberto P. Muñuzuri. 2024-12-18. Minimum nonlinearity for pattern-forming Turing instability in a mathematical autocatalytic model. https://arxiv.org/abs/2412.13783

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