Finite-time Lyapunov signatures of dynamical regimes in reservoir models

Abstract

Abstract: Although reservoir models are known to accurately predict critical transitions and regime changes, conventional analyses based on output time series or low-dimensional bifurcation structure fails to reveal the underlying mechanisms. This limitation arises because in high-dimensional reservoir space, qualitatively distinct pathways can yield similar outputs, obscuring the true nature of transitions. We show that finite-time Lyapunov exponent (FTLE) fills this gap by providing a dynamical measure sensitive to local stability within the reservoir. This is particularly crucial for transitions such as interior crises, where identifying collisions with unstable periodic orbits is practically infeasible in high dimensions. Using the logistic map as a canonical system, which apart from depicting interior crisis, exhibits intermittency, fully developed chaos, and crisis-induced transitions, we demonstrate that even when these regimes are not easily distinguishable in the reservoir state space using conventional methods, their FTLE distributions are faithfully reproduced. Our results establish FTLE as a systematic route to interpret high-dimensional reservoir models in terms of the underlying dynamical systems they emulate. © The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2026.