图灵扩散阈值在随机反应-扩散系统中的表现
Turing's diffusive threshold in random reaction-diffusion systems
AI总结：
研究探讨了在N>2的随机反应-扩散系统中，扩散阈值是否降低，从而允许真正的图灵不稳定性，并通过随机矩阵分析证明了多物种系统的复杂性。
摘要：
反应-扩散系统的图灵不稳定性只有在化学物质的扩散率足够不同的情况下才会出现。这个阈值在大多数N=2的系统中是不合理的，迫使实验实现不稳定性依赖于波动或额外的非扩散物质。本文受May对随机生态群落稳定性的分析启发，分析了反应-扩散系统中扩散阈值的概率分布，该系统由描述线性化动力学近似均匀固定点的随机矩阵定义。在可计算的N≤6情况下，发现随着N增加，扩散阈值更可能变小且合理，大多数多物种不稳定性无法用较少物种的简化模型描述。
英文摘要：
Turing instabilities of reaction-diffusion systems can only arise if the diffusivities of the chemical species are sufficiently different. This threshold is unphysical in most systems with $N=2$ diffusing species, forcing experimental realizations of the instability to rely on fluctuations or additional nondiffusing species. Here we ask whether this diffusive threshold lowers for $N>2$ to allow "true" Turing instabilities. Inspired by May's analysis of the stability of random ecological communities, we analyze the probability distribution of the diffusive threshold in reaction-diffusion systems defined by random matrices describing linearized dynamics near a homogeneous fixed point. In the numerically tractable cases $N\leqslant 6$, we find that the diffusive threshold becomes more likely to be smaller and physical as $N$ increases and that most of these many-species instabilities cannot be described by reduced models with fewer species.
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