Critical Transitions and Perturbation Growth Directions

Abstract

Critical transitions occur in a variety of dynamical systems. Here, we employ quantifiers of chaos to identify changes in the dynamical structure of complex systems preceding critical transitions. As suitable indicator variables for critical transitions, we consider changes in growth rates and directions of covariant Lyapunov vectors. Studying critical transitions in several models of fast-slow systems, i.e., a network of coupled FitzHugh-Nagumo oscillators, models for Josephson junctions and the Hindmarsh-Rose model, we find that tangencies between covariant Lyapunov vectors are a common and maybe generic feature during critical transitions. We further demonstrate that this deviation from hyperbolic dynamics is linked to the occurrence of critical transitions by using it as an indicator variable and evaluating the prediction success through receiver operating characteristic curves. In the presence of noise, we find the alignment of covariant Lyapunov vectors and changes in finite-time Lyapunov exponents to be more successful in announcing critical transitions than common indicator variables as, e.g., finite-time estimates of the variance. Additionally, we propose a new method for estimating approximations of covariant Lyapunov vectors without knowledge of the future trajectory of the system. We find that these approximated covariant Lyapunov vectors can also be applied to predict critical transitions.

References in corpus (9)

• Characterizing dynamics with covariant Lyapunov vectors
• Theory and computation of covariant Lyapunov vectors
• Hyperbolicity and the effective dimension of spatially-extended dissipative systems
• Structure of characteristic Lyapunov vectors in spatiotemporal chaos
• Laws of rare events for deterministic and random dynamical systems
• Towards a General Theory of Extremes for Observables of Chaotic Dynamical Systems
• Characteristic Lyapunov vectors in chaotic time-delayed systems
• Understanding and Controlling Regime Switching in Molecular Diffusion
• On the angle between the first and the second Lyapunov vectors in spatio-temporal chaos

Cited by in corpus (4)

• Stability analysis of chaotic systems from data
• Estimating covariant Lyapunov vectors from data
• A projector-based convergence proof of the Ginelli algorithm for covariant Lyapunov vectors
• Guidelines for data-driven approaches to study transitions in multiscale systems: the case of Lyapunov vectors