Detecting Regime Transitions in Dynamical Systems via the Mixup Euler Characteristic Profile

Fuente: arXiv

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Détails bibliographiques
Auteurs principaux:	Majhi, Sushovan, Mitra, Atish, Nandi, Santanu, Nurujjaman, Md, Sharma, Buddha Nath
Format:	Preprint
Publié:	2026
Sujets:	Dynamical Systems Algebraic Topology
Accès en ligne:	Acceder al recurso
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author	Majhi, Sushovan Mitra, Atish Nandi, Santanu Nurujjaman, Md Sharma, Buddha Nath
author_facet	Majhi, Sushovan Mitra, Atish Nandi, Santanu Nurujjaman, Md Sharma, Buddha Nath
contents	We develop a framework for detecting regime transitions in dynamical systems using the Mixup Euler Characteristic Profile (Mixup ECP) -- the Euler characteristic of the geometric intersection of ball unions around adjacent delay-embedded trajectory segments, viewed as a function of filtration scale. The Mixup ECP provides a detection statistic with a built-in null and guaranteed stability. We formalize regime detection as a low-side-permutation test, establish its validity and consistency, and introduce a multi-delay extension that automatically selects the most informative dynamical timescale. Complementing the topological signal with Complexity Variance, Higuchi fractal dimension, and a rolling mean baseline, the four-signal combined method achieves $9.50$ days MAE on Indian monsoon onset (Nepal target) -- a $32\%$ improvement over the rolling mean baseline and $9\%$ over CUSUM. Validated on the Lorenz system, logistic map, and three monsoon systems spanning both hemispheres (Indian/Nepal, Indian/Kerala, Western North Pacific), plus ENSO and a synthetic EEG dataset, the framework adds value precisely when the transition is gradual or obscured by noise.
format	Preprint
id	arxiv_https___arxiv_org_abs_2604_15262
institution	arXiv
publishDate	2026
record_format	arxiv
spellingShingle	Detecting Regime Transitions in Dynamical Systems via the Mixup Euler Characteristic Profile Majhi, Sushovan Mitra, Atish Nandi, Santanu Nurujjaman, Md Sharma, Buddha Nath Dynamical Systems Algebraic Topology We develop a framework for detecting regime transitions in dynamical systems using the Mixup Euler Characteristic Profile (Mixup ECP) -- the Euler characteristic of the geometric intersection of ball unions around adjacent delay-embedded trajectory segments, viewed as a function of filtration scale. The Mixup ECP provides a detection statistic with a built-in null and guaranteed stability. We formalize regime detection as a low-side-permutation test, establish its validity and consistency, and introduce a multi-delay extension that automatically selects the most informative dynamical timescale. Complementing the topological signal with Complexity Variance, Higuchi fractal dimension, and a rolling mean baseline, the four-signal combined method achieves $9.50$ days MAE on Indian monsoon onset (Nepal target) -- a $32\%$ improvement over the rolling mean baseline and $9\%$ over CUSUM. Validated on the Lorenz system, logistic map, and three monsoon systems spanning both hemispheres (Indian/Nepal, Indian/Kerala, Western North Pacific), plus ENSO and a synthetic EEG dataset, the framework adds value precisely when the transition is gradual or obscured by noise.
title	Detecting Regime Transitions in Dynamical Systems via the Mixup Euler Characteristic Profile
topic	Dynamical Systems Algebraic Topology
url	https://arxiv.org/abs/2604.15262