Nonlinearity-generated resilience in large complex systems

TY - JOUR

T1 - Nonlinearity-generated resilience in large complex systems

AU - Belga Fedeli, Sirio

AU - Fyodorov, Yan

AU - Ipsen, J R

N1 - 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.

PY - 2021/2/1

Y1 - 2021/2/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85101286743&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.103.022201

DO - 10.1103/PhysRevE.103.022201

M3 - Article

VL - 103

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 2

M1 - 022201

ER -