具有分段动力学调制的反应扩散系统中斑图形成：非均相动力学的一个实例研究
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics
摘要：
对模式涌现的研究以及对图灵模型的探索正在从理论和实验两个方面得到复兴。在这里，我们通过探索分段恒定动力学参数内的跳跃不连续性的影响，使用各种方法来识别和确认扩散驱动的不稳定条件，实现了空间相关反应动力学的稳定性分析。本质上，图灵模型中稳定性或不稳定性的存在是分段恒定动力学参数的局部性质，因此可以局部分析。特别是，参数是否在图灵空间内的局部评估提供了一个强有力的指示，即对于具有这些参数的足够大的区域，可以激发不稳定性。
英文摘要：
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction kinetics by exploring the effect of a jump discontinuity within piece-wise constant kinetic parameters, using various methods to identify and confirm the diffusion-driven instability conditions. Essentially, the presence of stability or instability in Turing models is a local property for piece-wise constant kinetic parameters and, as such, may be analysed locally. In particular, a local assessment of whether parameters are within the Turing space provides a strong indication that for a large enough region with these parameters, an instability can be excited.
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