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.

中文翻译：

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生态网络中的临界点和噪声引起的瞬变

跨学科研究中一个具有挑战性和突出的问题是了解高维动力系统中瞬态和随机性之间的相互作用。关注由经验数据构建的生态学中复杂互惠网络中的临界点动态，我们研究了噪声引起的崩溃和噪声引起的恢复现象。研究了两种类型的噪声：环境（高斯白）噪声和状态相关的人口统计噪声。造成这两种现象的动力机制是从一种稳定状态到另一种由随机强迫驱动的过渡，由不稳定的稳定状态介导。利用现实世界互惠网络的通用且有效的二维简化模型，我们发现平均瞬态寿命与噪声幅度呈代数关系，环境和人口噪声。我们通过分析从一个稳态到另一个稳态的平均第一次通过时间，对标度定律有了物理上的理解。噪声引起的崩溃和恢复现象以及相关的缩放规律对管理高维生态系统有影响。