空间扩展生态系统噪声恢复的普遍性
Universality of noise-induced resilience restoration in spatially-extended ecological systems
摘要：
许多系统可能由于内部故障或外部扰动而切换到不期望的状态，其中向退化生态系统状态的关键转变是一个突出的例子。弹性恢复的重点是空间扩展系统的能力和所需的时间来恢复到其期望的状态下随机环境条件。虽然平均场方法可以通过指示使不期望的状态不稳定所需的条件来指导恢复策略，但这些方法不能准确地捕获随机环境中空间扩展系统向期望状态的过渡过程。困难的根源在于缺乏数学工具来分析具有高维、非线性和随机效应的系统。我们通过开发新的数学工具来弥合这一差距，这些工具在空间嵌入式系统中采用成核理论来推进弹性恢复。我们研究我们的方法系统互惠动力学和扩散模型，发现系统可能会表现出单集群或多集群阶段，这取决于它们的大小和噪声强度，也构造了一个新的比例律在二维系统中的任意系统大小和噪声强度的恢复时间。这一方法不仅限于生态系统，而且适用于从生物学到基础设施系统的各种动力系统。
英文摘要：
Many systems may switch to an undesired state due to internal failures or external perturbations, of which critical transitions toward degraded ecosystem states are a prominent example. Resilience restoration focuses on the ability of spatially-extended systems and the required time to recover to their desired states under stochastic environmental conditions. While mean-field approaches may guide recovery strategies by indicating the conditions needed to destabilize undesired states, these approaches are not accurately capturing the transition process toward the desired state of spatially-extended systems in stochastic environments. The difficulty is rooted in the lack of mathematical tools to analyze systems with high dimensionality, nonlinearity, and stochastic effects. We bridge this gap by developing new mathematical tools that employ nucleation theory in spatially-embedded systems to advance resilience restoration. We examine our approach on systems following mutualistic dynamics and diffusion models, finding that systems may exhibit single-cluster or multi-cluster phases depending on their sizes and noise strengths, and also construct a new scaling law governing the restoration time for arbitrary system size and noise strength in two-dimensional systems. This approach is not limited to ecosystems and has applications in various dynamical systems, from biology to infrastructural systems.
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