Stability threshold approach for complex dynamical systems

TL;DR

This paper introduces the stability threshold (ST), a new measure for assessing the robustness of complex dynamical systems against large perturbations, by identifying the weakest perturbation capable of causing system failure.

Contribution

It proposes a novel stability measure, the stability threshold, along with a computational algorithm to quantify it, applicable across various complex systems.

Findings

The stability threshold effectively identifies the most vulnerable perturbation directions.

The approach provides valuable insights into system robustness.

Demonstrated applicability across multiple fields.

Abstract

A new measure to characterize stability of complex dynamical systems against large perturbation is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable to disrupt the system and switch it to an undesired dynamical regime. In the phase space, the stability threshold corresponds to the "thinnest site" of the attraction basin and therefore indicates the most "dangerous" direction of perturbations. We introduce a computational algorithm for quantification of the stability threshold and demonstrate that the suggested approach is effective and provides important insights. The generality of the obtained results defines their vast potential for application in such fields as engineering, neuroscience, power grids, Earth science and many others where robustness of complex systems is studied.