ArticleProceedings. Mathematical, physical, and engineering sciences2021
A closed form for Jacobian reconstruction from time series and its application as an early warning signal in network dynamics.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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5 citing papers in PubMed.
- Navigating tipping points: A complex systems framework for anticipating lake ecosystem collapse.Fundamental research · 2026Review
- Quantifying the intra- and inter-species community interactions in microbiomes by dynamic covariance mapping.Nature communications · 2025Article
- Exploring glioma heterogeneity through omics networks: from gene network discovery to causal insights and patient stratification.BioData mining · 2024Article
- Whole-brain modelling identifies distinct but convergent paths to unconsciousness in anaesthesia and disorders of consciousness.Communications biology · 2022Article
- Generalized Structural Kinetic Modeling: A Survey and Guide.Frontiers in molecular biosciences · 2022Review
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4 authors.
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Abstract
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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