In many asymptotically stable fluid systems, arbitrarily small fluctuations can grow by orders of magnitude before eventually decaying, dramatically enhancing the fluctuation variance beyond the minimum predicted by linear stability theory. Here using influential quantitative models drawn from the mathematical biology literature, we establish that dramatic amplification of arbitrarily small fluctuations is found in excitable cell signaling systems as well. Our analysis highlights how positive and negative feedback, proximity to bifurcations, and strong separation of timescales can generate nontrivial fluctuations without nudging these systems across their excitation thresholds. These insights, in turn, are relevant for a broader range of related oscillatory, bistable, and pattern-forming systems that share these features. The common thread connecting all of these systems with fluid dynamical examples of noise amplification is non-normality.

中文翻译：

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低于可激发细胞信号传导阈值的非平凡扩增

在许多渐近稳定的流体系统中，任意小的波动在最终衰减之前可以增长几个数量级，从而大大提高了波动方差，超出了线性稳定性理论所预测的最小值。在这里，使用从数学生物学文献中提取的有影响力的定量模型，我们建立了在可激发细胞信号系统中也发现了任意微小波动的急剧放大。我们的分析强调了正反馈和负反馈，与分叉点的接近以及时间尺度的强烈分离如何能够产生不重要的波动，而不会在这些系统的激励阈值上拖累这些系统。这些见解又与共享这些功能的更广泛的相关振荡，双稳态和模式形成系统有关。