Constrained basin stability for studying transient phenomena in dynamical systems

TL;DR

This paper introduces constrained basin stability (CBS), a new method for analyzing transient phenomena in dynamical systems, demonstrated through applications to the Lorenz system and Earth's carbon cycle model.

Contribution

The paper presents CBS as a novel extension of basin stability that accounts for transient dynamics, enhancing early warning capabilities and stability analysis in complex systems.

Findings

CBS detects precursory phenomena of boundary crisis bifurcation in the Lorenz system.

CBS provides a return time-dependent stability measure for Earth's carbon cycle model.

CBS complements traditional stability analyses by focusing on transient behaviors.

Abstract

Transient dynamics are of large interest in many areas of science. Here, a generalization of basin stability (BS) is presented: constrained basin stability (CBS) that is sensitive to various different types of transients arising from finite size perturbations. CBS is applied to the paradigmatic Lorenz system for uncovering nonlinear precursory phenomena of a boundary crisis bifurcation. Further, CBS is used in a model of the Earth's carbon cycle as a return time-dependent stability measure of the system's global attractor. Both case studies illustrate how CBS's sensitivity to transients complements BS in its function as an early warning signal and as a stability measure. CBS is broadly applicable in systems where transients matter, from physics and engineering to sustainability science. Thus, CBS complements stability analysis with BS as well as classical linear stability analysis and will be a useful tool for many applications.