Geometric Transition of Latent Dynamics in Intermittent Chaos: SVD-based Effective Dimension for Detection and Proactive Control
Abstract
This paper investigates the geometric detection of latent dynamic transitions (where the latent space is defined as a finite-dimensional state space reconstructed via a delay-embedding Hankel matrix) in mutually coupled phase-locked loops (PLLs) exhibiting on-off intermittent chaos. We propose a data-driven approach to identify the transition of the effective dimension in latent dynamics as a precursor to physical bursting events. By applying Singular Value Decomposition (SVD) to a Hankel matrix constructed from high-resolution oversampled data, we extract the effective dimension that reflects the dynamical shift of intrinsic variables - from a synchronized two-dimensional manifold to a higher-dimensional chaotic state - prior to the actual burst. This geometric indicator enables a proactive, event-driven intervention using Pyragas-type delayed feedback control, which is activated only when the detected dimension exceeds a critical threshold. Simulation results demonstrate that this geometric precursor effectively compensates for control latencies and substantially reduces accumulated control energy compared to conventional continuous feedback. The findings establish a methodological strategy for stabilizing infinite-dimensional delayed systems by exploiting early warning signals embedded in dimensional transitions of latent dynamics.
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BibTeX
@misc{hikihara2026geometric,
title = {{Geometric Transition of Latent Dynamics in Intermittent Chaos: SVD-based Effective Dimension for Detection and Proactive Control}},
author = {Takashi Hikihara and Tetsushi Saburi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16495},
eprint = {2610.16495},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16495},
}
RIS
TY - UNPB
TI - Geometric Transition of Latent Dynamics in Intermittent Chaos: SVD-based Effective Dimension for Detection and Proactive Control
AU - Takashi Hikihara
AU - Tetsushi Saburi
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.16495
UR - https://arxiv.org/abs/2610.16495
AB - This paper investigates the geometric detection of latent dynamic transitions (where the latent space is defined as a finite-dimensional state space reconstructed via a delay-embedding Hankel matrix) in mutually coupled phase-locked loops (PLLs) exhibiting on-off intermittent chaos. We propose a data-driven approach to identify the transition of the effective dimension in latent dynamics as a precursor to physical bursting events. By applying Singular Value Decomposition (SVD) to a Hankel matrix constructed from high-resolution oversampled data, we extract the effective dimension that reflects the dynamical shift of intrinsic variables - from a synchronized two-dimensional manifold to a higher-dimensional chaotic state - prior to the actual burst. This geometric indicator enables a proactive, event-driven intervention using Pyragas-type delayed feedback control, which is activated only when the detected dimension exceeds a critical threshold. Simulation results demonstrate that this geometric precursor effectively compensates for control latencies and substantially reduces accumulated control energy compared to conventional continuous feedback. The findings establish a methodological strategy for stabilizing infinite-dimensional delayed systems by exploiting early warning signals embedded in dimensional transitions of latent dynamics.
ER -