What is it about?

Dynamical systems are used to model power grids, the brain, climate, and many other natural systems. Most dynamical systems display multistabilitiy, which means that there could be several coexisting stable states, also known as "attractors". For example, the glacial "ice-ages" and the current "warm Earth" can be viewed as two attractors of the Earth climate system. Our work provides a computational framework to analyze such multistable dynamical systems, in terms of the global (or basin) stability of the individual attractors in the system. The framework is accompanied by an easy to use high-performance code base to perform such analysis within only a couple lines of code.

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Why is it important?

Global (or basin) stability is very important for the concept of tipping points: transitions of a dynamical system from one attractor to another. There, it is important to quantify how the system may respond to finite perturbations. Insofar, the only accessible way to characterize stability of dynamical systems was via the local stability, which only describes the response of the system to infinitesimal perturbations. However, for studying tipping points, and other related phenomena, one needs to know how the system responds to finite perturbations. This is the kind of information that global stability offers. Hence, our framework complements this established standard and allows expanding stability analysis into a realm that deals with finite perturbations. We believe our work will accelerate research on multistability and tipping points.


It was a great pleasure to work on this paper. This paper has been developed in the most "open science" way possible: most of the work of this project has been done on GitHub in the form of Pull Requests. This was an exciting experience! The most pleasant part of this work was designing an interface that can last the test of time: even if new approaches are developed in the future, we tried to create an interface that is extendable so that it can include new approaches instead of being more and more obsolete as new research comes out.

George Datseris

Read the Original

This page is a summary of: Framework for global stability analysis of dynamical systems, Chaos An Interdisciplinary Journal of Nonlinear Science, July 2023, American Institute of Physics, DOI: 10.1063/5.0159675.
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