Dynamical systems and complex networks: A Koopman operator perspective

• URL: http://arxiv.org/abs/2405.08940v2
• Date: Mon, 16 Dec 2024 08:28:23 GMT
• Title: Dynamical systems and complex networks: A Koopman operator perspective
• Authors: Stefan Klus, Nataša Djurdjevac Conrad,
• Abstract summary: Koopman operator has entered many research areas in the last years. We show how the underlying concept$representing nonlinear systems by infinite networks can be transformed into Laplacians.
• Score: 0.9714447724811842
• License:
• Abstract: The Koopman operator has entered and transformed many research areas over the last years. Although the underlying concept$\unicode{x2013}$representing highly nonlinear dynamical systems by infinite-dimensional linear operators$\unicode{x2013}$has been known for a long time, the availability of large data sets and efficient machine learning algorithms for estimating the Koopman operator from data make this framework extremely powerful and popular. Koopman operator theory allows us to gain insights into the characteristic global properties of a system without requiring detailed mathematical models. We will show how these methods can also be used to analyze complex networks and highlight relationships between Koopman operators and graph Laplacians.

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