Framework for global stability analysis of dynamical systems

Dynamical systems that are used to model power grids, the brain, and other physical systems can exhibit coexisting stable states known as attractors. A powerful tool to understand such systems, as well as to better predict when they may tip from one stable state to the other, is global stability analysis. It involves identifying the initial conditions that converge to each attractor, known as the basins of attraction, measuring the relative volume of these basins in state space, and quantifying how these fractions change as a system parameter evolves. By improving existing approaches, we present a comprehensive framework that allows for global stability analysis of dynamical systems. Notably, our framework enables the analysis to be made efficiently and conveniently over a parameter range. As such, it becomes an essential tool for stability analysis of dynamical systems that goes beyond local stability analysis offered by alternative frameworks. We demonstrate the effectiveness of our approach on a variety of models, including climate, power grids, ecosystems, and more. Our framework is available as simple-to-use open-source code as part of the DynamicalSystems.jl library.

Automated summary

This paragraph describes the existence of coexisting stable states called attractors in dynamical systems used to model power grids, the brain, and other physical systems. Global stability analysis is a powerful tool to understand these systems and predict transitions between stable states. The authors present an improved framework that allows for efficient and convenient global stability analysis over a parameter range, going beyond local stability analysis offered by other frameworks.