论文标题
图灵的扩散阈值在随机反应扩散系统中
Turing's diffusive threshold in random reaction-diffusion systems
论文作者
论文摘要
反应扩散系统的图灵不稳定性只有在化学物种的扩散性足够不同的情况下才会出现。在大多数具有$ n = 2 $扩散物种的系统中，该阈值是非物理的，迫使不稳定的实验实现依靠波动或其他非灭菌物种。在这里，我们询问此扩散阈值是否以$ n> 2 $降低，以允许“真正的”图灵不稳定性。受到May对随机生态群落稳定性的分析的启发，我们分析了由随机矩阵定义的反应扩散阈值的概率分布，这些矩阵由随机矩阵定义，这些矩阵描述了均匀固定点附近的线性化动力学。在数字上可处理的情况下，$ n \ leqslant 6 $，我们发现扩散阈值更容易变小，并且随着$ n $的增加而变得更小，而且物理的增加，并且大多数这些多种物种不稳定性无法通过较少物种的减少模型来描述。
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.
