论文标题
大型随机动力系统的波动光谱揭示了生态网络中的隐藏结构
Fluctuation spectra of large random dynamical systems reveal hidden structure in ecological networks
论文作者
论文摘要
了解大型动力学系统（例如生态系统）中的复杂性与稳定之间的关系仍然是复杂性理论中的一个关键开放问题，它启发了五十多年来发展的丰富工作。该理论的绝大多数都解决了平衡点周围的渐近线性稳定性，但实际上“稳定性”的概念在经验生态文献中还有其他用途。 “时间稳定性”的重要概念描述了由内在或外在噪声驱动的人口动态波动的特征。在这里，我们将随机矩阵理论的工具应用于时间稳定性问题，从而得出了复杂生态网络波动光谱的分析预测。我们表明，不同的网络结构在波动范围内留下了不同的签名，并证明了我们的理论在浮游生物丰度的分析生态时间内数据中的应用。
Understanding the relationship between complexity and stability in large dynamical systems -- such as ecosystems -- remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty years. The vast majority of this theory addresses asymptotic linear stability around equilibrium points, but the idea of `stability' in fact has other uses in the empirical ecological literature. The important notion of `temporal stability' describes the character of fluctuations in population dynamics, driven by intrinsic or extrinsic noise. Here we apply tools from random matrix theory to the problem of temporal stability, deriving analytical predictions for the fluctuation spectra of complex ecological networks. We show that different network structures leave distinct signatures in the spectrum of fluctuations, and demonstrate the application of our theory to the analysis ecological timeseries data of plankton abundances.
