AI 中文总结
本文推导了任意组分一维反应扩散系统Turing分岔的振幅方程至五阶规范形，并实现于Python包及Mathematica程序，可检测两余维点，适用于交叉扩散、高阶标量方程及四组分系统等案例。
AI 中文摘要
本文推导了在一维空间中含有任意数量组分的反应扩散方程组在Turing分岔点处振幅方程的一般表达式。规范形计算至五阶，从而能够检测和分析分岔临界性发生变化的两余维点。这些表达式已在Python包中实现，用户只需指定反应动力学表达式和扩散常数值。该代码还配有Mathematica程序，用于在参数平面内计算Turing分岔曲线并自动检测两余维点。通过多个实例展示了该方法的通用性，包括一个含交叉扩散的案例、一个高阶标量方程以及一个四组分系统。
英文摘要
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.
Journal refEdgardo Villar-Sepúlveda and Alan Champneys. 2023. Computation of Turing Bifurcation Normal Form for n-Component Reaction-Diffusion Systems. ACM Trans. Math. Softw. 49, 4, Article 35 (December 2023)
DOI：10.1145/3625560
