This article describes a reduction of a non-autonomous Brusselator reaction–diffusion system of partial differential equations on a spherical cap with time-dependent curvature using the method of centre manifold reduction. Parameter values are chosen such that the change in curvature would cross critical values which would change the stability of the patternless solution in the constant domain case. The evolving domain functions and quasi-patternless solutions are derived as well as a method to obtain this non-autonomous normal form. The coefficients of such a normal form are computed and the reduction solutions are compared to numerical solutions.

中文翻译：

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在缓慢变平的球形帽中形成图案：延迟分叉

本文介绍了使用中心流形缩减方法对具有时间相关曲率的球冠上的非自治Brusselator反应-扩散系统的偏微分方程的简化。选择参数值，以使曲率变化将越过临界值，这将改变恒定域情况下无图案解决方案的稳定性。导出了演化中的域函数和拟无模式解，以及一种获得这种非自治范式的方法。计算这种标准形式的系数，并将简化解与数值解进行比较。