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  • Letter
  • Open Access

Predicting the response of structurally altered and asymmetrical networks

Melvyn Tyloo

  • Living Systems Institute, University of Exeter, Exeter EX4 4QD,United Kingdom and Department of Mathematics and Statistics, Faculty of Environment, Science, and Economy, University of Exeter, Exeter EX4 4QD, United Kingdom

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Phys. Rev. E 112, L042301 – Published 10 October, 2025

DOI: https://doi.org/10.1103/3s3d-qr4l

Abstract

We investigate how the response of coupled dynamical systems is modified due to a structural alteration of the interaction. The majority of the literature focuses on additive perturbations and symmetrical interaction networks. Here, we consider the challenging problem of multiplicative structural alterations and asymmetrical interaction coupling. We introduce a framework to approximate the averaged response at each network node for general structural alterations, including non-normal and asymmetrical ones. Our findings indicate that both the asymmetry and non-normality of the structural alterations impact the global and local responses at different orders in time. We propose a set of matrices to identify the nodes whose response is affected the most by the structural alteration.

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Phys. Rev. E 112, L042301– Published 10 October, 2025
  • Received 16 June 2025
  • Accepted 4 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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