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arXiv · 2301.12966

Lyapunov Exponents for Temporal Networks

Annalisa Caligiuri·Victor M. Eguiluz·Leonardo di Gaetano·Tobias Galla·Lucas Lacasa
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Abstract

By interpreting a temporal network as a trajectory of a latent graph dynamical system, we introduce the concept of dynamical instability of a temporal network, and construct a measure to estimate the network Maximum Lyapunov Exponent (nMLE) of a temporal network trajectory. Extending conventional algorithmic methods from nonlinear time-series analysis to networks, we show how to quantify sensitive dependence on initial conditions, and estimate the nMLE directly from a single network trajectory. We validate our method for a range of synthetic generative network models displaying low and high dimensional chaos, and finally discuss potential applications.

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Annalisa Caligiuri, Victor M. Eguiluz, Leonardo di Gaetano, Tobias Galla, Lucas Lacasa. 2023-01-30. Lyapunov Exponents for Temporal Networks. https://doi.org/10.1103/physreve.107.044305

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