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arXiv · 2609.28039

Computation of Turing bifurcation normal form for n-component reaction-diffusion systems

Edgardo Villar-Sepúlveda·Alan R. Champneys
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Abstract

General expressions are derived for the amplitude equation valid at a Turing bifurcation of a system of reaction-diffusion equations in one spatial dimension, with an arbitrary number of components. The normal form is computed up to fifth order, which enables the detection and analysis of codimension-two points where the criticality of the bifurcation changes. The expressions are implemented within a Python package, in which the user needs to specify only expressions for the reaction kinetics and the values of diffusion constants. The code is augmented with a Mathematica routine to compute curves of Turing bifurcations in a parameter plane and automatically detect codimension-two points. The software is illustrated with examples that show the versatility of the method including a case with cross-diffusion, a higher-order scalar equation, and a four-component system.

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Edgardo Villar-Sepúlveda, Alan R. Champneys. 2026-09-23. Computation of Turing bifurcation normal form for n-component reaction-diffusion systems. https://doi.org/10.1145/3625560

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