Tu Chengyi, D'Odorico Paolo, Suweis Samir
School of Ecology and Environmental Science, Yunnan University, 650091, Kunming, China.
Yunnan Key Laboratory of Plant Reproductive Adaptation and Evolutionary Ecology, 650091, Kunming, China.
iScience. 2020 Dec 9;24(1):101912. doi: 10.1016/j.isci.2020.101912. eCollection 2021 Jan 22.
One of the outstanding problems in complexity science and engineering is the study of high-dimensional networked systems and of their susceptibility to transitions to undesired states as a result of changes in external drivers or in the structural properties. Because of the incredibly large number of parameters controlling the state of such complex systems and the heterogeneity of its components, the study of their dynamics is extremely difficult. Here we propose an analytical framework for collapsing complex N-dimensional networked systems into an S+1-dimensional manifold as a function of S effective control parameters with S << N. We test our approach on a variety of real-world complex problems showing how this new framework can approximate the system's response to changes and correctly identify the regions in the parameter space corresponding to the system's transitions. Our work offers an analytical method to evaluate optimal strategies in the design or management of networked systems.
复杂性科学与工程领域的突出问题之一是对高维网络系统及其因外部驱动因素或结构特性变化而转变为非期望状态的敏感性进行研究。由于控制此类复杂系统状态的参数数量极其庞大且其组件具有异质性，对其动力学进行研究极为困难。在此，我们提出一个分析框架，可将复杂的N维网络系统折叠为一个S + 1维流形，该流形是S个有效控制参数的函数，其中S << N。我们在各种现实世界的复杂问题上测试了我们的方法，展示了这个新框架如何能够近似系统对变化的响应，并正确识别参数空间中与系统转变相对应的区域。我们的工作提供了一种分析方法，用于评估网络系统设计或管理中的最优策略。
