2026/04/26 by Dishant Sisodia, Sarika Jalan · 1 voice
Engineering · Mathematics · Physics and Astronomy · #Control theory (sociology) #Dynamical systems theory #Lyapunov exponent #Lyapunov function #Navier-Stokes equation solutions #Quantum chaos and dynamical systems #Stability (learning theory) #Stability and Controllability of Differential Equations #Trajectory #nlin.CD
paper · pdf · doi:10.1140/epjb/s10051-026-01204-4
arxiv created 2026/04/26 · arxiv published 2026/04/26 · arxiv updated 2026/04/26 · openalex publication_date 2026/06/01 · openalex created_date 2026/06/27 · openalex updated_date 2026/07/23
We use finite-time Lyapunov exponent (FTLE) distributions to probe transition mechanisms in high-dimensional reservoir maps trained on low-dimensional chaotic dynamics across multiple regimes. While trained reservoirs accurately predict critical transitions and regime shifts, conventional analyses based on time series or bifurcation structure provide limited mechanistic insight, since distinct pathways in high dimensions can yield similar outputs. We show that FTLE statistics overcome this limitation. This is particularly important for interior crises, where direct identification of unstable periodic orbit collisions in the reservoir space is infeasible. Using the logistic map as a canonical example exhibiting intermittency, fully developed chaos, and crisis-induced transitions, we demonstrate that although such distinct regimes are difficult to characterize within the high dimensional reservoir space, their FTLE distributions are faithfully reproduced. This establishes FTLE analysis as a systematic and reliable framework for uncovering transition mechanisms in learned reservoir dynamics.