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arXiv · 2604.15262

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

Sushovan Majhi·Atish Mitra·Santanu Nandi·Md Nurujjaman·Buddha Nath Sharma
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Abstract

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.

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Sushovan Majhi, Atish Mitra, Santanu Nandi, Md Nurujjaman, Buddha Nath Sharma. 2026-04-16. Detecting Regime Transitions in Dynamical Systems via the Mixup Euler Characteristic Profile. https://arxiv.org/abs/2604.15262

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