Institute for Complex Systems and Mathematical Biology, School of Natural and Computing Sciences, King's College, University of Aberdeen, Aberdeen AB24 3UE, UK.
School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA.
J R Soc Interface. 2020 Oct;17(171):20200645. doi: 10.1098/rsif.2020.0645. Epub 2020 Oct 14.
A challenging and outstanding problem in interdisciplinary research is to understand the interplay between transients and stochasticity in high-dimensional dynamical systems. Focusing on the tipping-point dynamics in complex mutualistic networks in ecology constructed from empirical data, we investigate the phenomena of noise-induced collapse and noise-induced recovery. Two types of noise are studied: environmental (Gaussian white) noise and state-dependent demographic noise. The dynamical mechanism responsible for both phenomena is a transition from one stable steady state to another driven by stochastic forcing, mediated by an unstable steady state. Exploiting a generic and effective two-dimensional reduced model for real-world mutualistic networks, we find that the average transient lifetime scales algebraically with the noise amplitude, for both environmental and demographic noise. We develop a physical understanding of the scaling laws through an analysis of the mean first passage time from one steady state to another. The phenomena of noise-induced collapse and recovery and the associated scaling laws have implications for managing high-dimensional ecological systems.
跨学科研究中的一个具有挑战性和突出的问题是理解高维动力系统中瞬变和随机性之间的相互作用。本研究聚焦于从经验数据构建的生态学中复杂共生网络的 tipping-point 动力学，研究噪声诱导崩溃和噪声诱导恢复现象。研究了两种噪声：环境（高斯白噪声）噪声和状态相关的人口噪声。这两种现象的动力学机制是由随机力驱动的从一个稳定的稳态到另一个稳定的稳态的转变，由不稳定的稳态介导。利用一个通用且有效的二维简化模型来研究真实世界的共生网络，我们发现对于环境噪声和人口噪声，平均瞬态寿命与噪声幅度呈代数关系。我们通过分析从一个稳态到另一个稳态的平均首次通过时间来理解标度律的物理意义。噪声诱导崩溃和恢复现象以及相关的标度律对管理高维生态系统具有重要意义。
