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Nonlinearity-generated resilience in large complex systems

Research output: Contribution to journalArticlepeer-review

Original languageEnglish
Article number022201
Number of pages16
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume103
Issue number2
DOIs
Accepted/In press8 Dec 2020
Published1 Feb 2021

Bibliographical note

Funding Information: We acknowledge support by the Engineering and Physical Sciences Research Council Centre for Doctoral Training in Cross-Disciplinary Approaches to Non-Equilibrium Systems through Grant No. EP/L015854/1 (S.B.F.) and by the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (J.R.I.). Publisher Copyright: © 2021 American Physical Society. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

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King's Authors

Abstract

We consider a generic nonlinear extension of May's 1972 model by including all higher-order terms in the expansion around the chosen fixed point (placed at the origin) with random Gaussian coefficients. The ensuing analysis reveals that as long as the origin remains stable, it is surrounded by a “resilience gap”: there are no other fixed points within a radius r∗>0 and the system is therefore expected to be resilient to a typical initial displacement small in comparison to r∗. The radius r∗ is shown to vanish at the same threshold where the origin loses local stability, revealing a mechanism by which systems close to the tipping point become less resilient. We also find that beyond the resilience radius the number of fixed points in a ball surrounding the original point of equilibrium grows exponentially with N, making systems dynamics highly sensitive to far enough displacements from the origin.

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