A closed form for Jacobian reconstruction from time series and its application as an early warning signal in network dynamics.
A closed form for Jacobian reconstruction from time series and its application as an early warning signal in network dynamics.
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DOI：
10.1098/rspa.2020.0742
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发表时间：
2021-03
期刊：
影响因子：
--
通讯作者：
Gross T
中科院分区：
文献类型：
--
作者：
Barter E;Brechtel A;Drossel B;Gross T
动力系统的雅可比矩阵描述了它对扰动的响应。相反，可以通过仔细监测系统如何响应环境噪声来估计雅可比矩阵。我们提出了一个封闭形式的分析解决方案的计算系统的雅可比矩阵的时间序列。能够访问雅可比矩阵可以进行广泛的数学分析，从而可以更深入地了解系统。在这里，我们认为特别是领先的雅可比特征值的计算作为一个预警信号的关键转变。为了说明这种方法，我们将其应用到生态元食物网模型，这是强非线性动态多层网络。我们的分析表明，可以得到准确的结果，虽然该方法的数据要求仍然很高。
The Jacobian matrix of a dynamical system describes its response to perturbations. Conversely, one can estimate the Jacobian matrix by carefully monitoring how the system responds to environmental noise. We present a closed-form analytical solution for the calculation of a system’s Jacobian from a time series. Being able to access the Jacobian enables a broad range of mathematical analyses by which deeper insights into the system can be gained. Here we consider in particular the computation of the leading Jacobian eigenvalue as an early warning signal for critical transitions. To illustrate this approach, we apply it to ecological meta-foodweb models, which are strongly nonlinear dynamical multi-layer networks. Our analysis shows that accurate results can be obtained, although the data demand of the method is still high.
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影响因子：
4.7
作者：
Moradkhani, H;Sorooshian, S;Houser, PR
通讯作者：
Houser, PR
影响因子：
2.4
作者：
Gross, T;Feudel, U
通讯作者：
Feudel, U
影响因子：
3.7
作者：
Dakos V;Carpenter SR;Brock WA;Ellison AM;Guttal V;Ives AR;Kéfi S;Livina V;Seekell DA;van Nes EH;Scheffer M
通讯作者：
Scheffer M
影响因子：
4.8
作者：
Clark, JS
通讯作者：
Clark, JS
影响因子：
6.1
作者：
Ives, AR;Dennis, B;Carpenter, SR
通讯作者：
Carpenter, SR