论文标题
网络关键减速：数据驱动的非线性网络中关键过渡的检测
Network Critical Slowing Down: Data-Driven Detection of Critical Transitions in Nonlinear Networks
论文作者
论文摘要
在自然文章中，Scheffer等人。提出了一个新颖的数据驱动框架，以预测复杂系统中的关键转变。这些过渡可能源于失败，退化或对抗性作用，这归因于非线性动力学中的分叉。他们的方法建立在关键放慢速度的现象上，即，响应分叉附近的小扰动而缓慢恢复。我们扩展了他们在非线性网络中检测和定位关键转变的方法。通过引入网络关键减速的概念，本文的目的是检测网络仅通过分析其测量数据来分析其签名即可进行分叉。我们专注于两类广泛使用的非线性网络：（1）用于同步耦合振荡器的库拉莫托模型，以及（2）群中的吸引力 - 抑制动力学，每种动力学都会呈现特定类型的分叉类型。基于关键减慢的现象，我们研究了扰动系统的渐近行为并接近分叉，并利用这一事实来开发一种确定性的方法来检测和识别非线性网络中的关键过渡。此外，我们研究了经过随机噪声过程的状态协方差矩阵，并接近分叉，并使用它来开发一个随机框架来检测关键过渡。我们的仿真结果显示了方法的优势和局限性。
In a Nature article, Scheffer et al. presented a novel data-driven framework to predict critical transitions in complex systems. These transitions, which may stem from failures, degradation, or adversarial actions, have been attributed to bifurcations in the nonlinear dynamics. Their approach was built upon the phenomenon of critical slowing down, i.e., slow recovery in response to small perturbations near bifurcations. We extend their approach to detect and localize critical transitions in nonlinear networks. By introducing the notion of network critical slowing down, the objective of this paper is to detect that the network is undergoing a bifurcation only by analyzing its signatures from measurement data. We focus on two classes of widely-used nonlinear networks: (1) Kuramoto model for the synchronization of coupled oscillators and (2) attraction-repulsion dynamics in swarms, each of which presents a specific type of bifurcation. Based on the phenomenon of critical slowing down, we study the asymptotic behavior of the perturbed system away and close to the bifurcation and leverage this fact to develop a deterministic method to detect and identify critical transitions in nonlinear networks. Furthermore, we study the state covariance matrix subject to a stochastic noise process away and close to the bifurcation and use it to develop a stochastic framework for detecting critical transitions. Our simulation results show the strengths and limitations of the methods.
