arXiv subjects

N'Gbo N'Gbo

Publications and source records attributed to N'Gbo N'Gbo.

4 recordsLinked to original sources

arXiv2026

Equation-Free Screening of Mittag-Leffler-Compatible Dynamics from Scalar Time Series via kNN Multi-Horizon Profiles

Fractional models provide a natural description of systems with memory, but a noninteger derivative should not be introduced solely because a time series is curved or slowly relaxing. We develop an equation-free preliminary screening framework that asks whether a scalar time series produces a multi-horizon k-nearest-neighbor (kNN) profile more compatible with Mittag-Leffler-type behavior than with selected conventional alternatives. In an ideal matched Caputo-relaxation benchmark, the complete generation-kNN-profile-model-comparison pipeline reproduces the expected Mittag-Leffler geometry and recovers the generating order to within approximately $10^{-3}$; this is interpreted as controlled calibration rather than as general fractional-order identification. Under 3% trajectory-specific observational noise, the held-out Mittag-Leffler preference is most consistent when the generating dynamics are well separated from the integer-order limit and becomes progressively less decisive as $α\rightarrow1$. The fitted order $α_{\mathrm{fit}}$, however, shows substantially larger realization-to-realization variability. Thus, relative model compatibility is more robust than single-realization order estimation in the present noisy benchmark. Noise-free nonfractional controls show a separate limitation of specificity: a stretched exponential can generate a strongly Mittag-Leffler-compatible profile, whereas inclusion of the generating rational/Hill family recovers that family and its parameters to numerical precision in the matched setting. A positive Mittag-Leffler-versus-exponential screen therefore does not uniquely establish fractional origin. A fractional chaotic system is treated only as an exploratory extension: the Mittag-Leffler growth family gives lower finite-window RMSE than exponential and logistic/saturating alternatives over the detected pre-transition interval.

math.DS↗

arXiv2026

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles

Estimating positive largest Lyapunov exponents from data is comparatively natural because neighboring trajectories separate, whereas stable dynamics require resolving contraction before measurement noise or finite precision erases the signal. We introduce a period-aware forecast-error contraction procedure for estimating a dominant negative Lyapunov exponent from ensembles of short scalar trajectories without using governing equations or an analytical Jacobian. A k-nearest-neighbor predictor is trained on trajectory histories, the geometric-mean absolute forecast error is evaluated at phase-consistent horizons, and the exponent is obtained from the slope of the logarithmic error profile. Unlike data-driven approaches that reconstruct local evolution matrices or differentiate a learned surrogate, the proposed method extracts the contraction rate directly from out-of-sample forecast errors. Two adaptations are essential: the forecast step is synchronized with the detected orbit period, and candidate slopes are accepted only when they form a stable consensus across several transient lengths. On the logistic map, the method recovers 92 of 112 negative-exponent parameter values with a mean absolute error of 0.0253 and $R^2=0.886$. On a two-dimensional map without fixed points, independent scalar pipelines based on the three observables $x_n$, $y_n$, and $z_n$ give mean absolute errors of 0.00879--0.01145 and $R^2=0.983$--$0.986$. Because the estimation stage uses only observed trajectories, the framework provides a basis for repeated-relaxation experiments in which short sensor responses are available but the governing equations and analytical Jacobian are unknown. Experimental validation remains a subject of future work.

nlin.CD↗

arXiv2026

FEG-Pro: Forecast-Error Growth Profiling for Finite-Horizon Instability Analysis of Nonlinear Time Series

Estimating the largest Lyapunov exponent from a scalar time series is difficult when the governing equations, tangent dynamics, and full state vector are unavailable. We propose FEG-Pro, a forecast-error growth profiling framework for nonlinear scalar time series. The method constructs autocorrelation-guided sparse histories, performs distance-weighted k-nearest-neighbor multi-horizon forecasting, and analyzes the logarithmic growth of geometrically averaged forecast errors. Its primary output is the finite-horizon forecast-error growth slope, lambda_FEG. When the error-growth curve supports a quasi-linear regime, this slope can be compared with reference largest Lyapunov exponents as an estimate of the dominant instability rate. The same pipeline also extracts the formal fit-selection regime, curvature, residual roughness after quadratic detrending, monotonicity, and forecast-error distribution entropy (FEDE) from signed multi-horizon errors. These secondary descriptors are intended not only as diagnostic controls for the slope, but also as candidate machine-learning features for nonlinear signal analysis, because they encode profile geometry and distributional uncertainty not captured by lambda_FEG alone. We evaluate the method on chaotic maps, Mackey-Glass delay dynamics, and scalar Lorenz-63 observables with known or reference exponents. Full-record experiments show good agreement in quasi-linear cases and meaningful curve-shape information in curved or weak profiles. A dyadic length-halving experiment on representative logistic, Mackey-Glass, and Lorenz records shows that residual roughness and mean FEDE often change monotonically and remain interpretable as record length decreases, even when the slope becomes biased or highly variable. The results support treating forecast-error growth as a structured profile and feature-generation framework rather than a single-number estimator.

nlin.CD↗

arXiv2022

Traveling waves of a generalized Rotation-Camassa-Holm equation with the Coriolis effect

In this paper, we analyze the dynamics of a generalized Rotation-Camassa-Holm equation, which is the $θ$-equation augmented with the Coriolis effect, induced by the earth rotation. The generalized Rotation-Camassa-Holm equation (named as Rotation-$θ$ equation) is a generalization of a family of models (including the Rotation-Camassa-Holm equation for $θ=\frac{1}{3}$, asymptotic Rotation-Camassa-Holm equation for $θ=1$ and the Rotation-Degasperis-Procesi (DP) equation for $θ=\frac{1}{4}$). Our study is conducted via the bifurcation method and qualitative theory of dynamical systems. The existence of not only smooth solitary wave solutions, periodic wave solutions, but also peakons and periodic peakon solutions is shown. The chosen values $θ$, allow us to assess the difference in behavior between the classical $θ$-equation and the Rotation-$θ$ equation. We conclude that the Coriolis effect does affect the traveling wave solutions. We summarize the bifurcations and explicit expressions of waves solutions in three theorems in Section 4. A conclusion ends the paper.

math-ph↗