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RESEARCH ARTICLE

Parametric analysis and statistical characterization of extreme events in a minimal Lorenz-like chaotic system

Jianning Huang1* ,  Paul Didier Kamdem Kuate2 ,  Achille Ecladore Tchahou Tchendjeu3
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1 School of Mathematics and Information Science, Nanchang Normal University, Nanchang, Jiangxi, China
2 Department of Electrical and Power Engineering, Higher Technical Teachers Training College, University of Bamenda, Bambili, Northwest Region, Cameroon
3 Department of Electrical and Electronic Engineering, National Polytechnic Institute, University of Bamenda, Bambili, Northwest Region, Cameroon
NSCE, 025450017 https://doi.org/10.36922/NSCE025450017
Received: 3 November 2025 | Revised: 28 November 2025 | Accepted: 5 December 2025 | Published online: 24 December 2025
© 2025 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

Extreme events are rare, high-impact phenomena that deviate significantly from nominal behavior, posing significant challenges across both natural and engineered systems, from climate dynamics to neurological conditions. The present study investigates the intricate dynamics and emergence of extreme events in a minimal, nonhyperbolic Lorenz-like chaotic system, characterized by piecewise linear nonlinearities. By leveraging standard nonlinear analysis and statistical tools, we explore how the system parameters govern its dynamical transitions, amplitude control, and propensity for extreme events. For small values of the control parameter, the system exhibits chaotic behavior, characterized by frequent, high-amplitude excursions indicative of extreme events. Statistical analyses of local maxima and inter-event intervals further characterize these events, highlighting their rarity and high magnitude through heavy-tailed probability distributions. The simplicity and controllability of the proposed model make it a valuable tool for theoretical exploration and practical applications in fields such as climate modeling, engineering, and nonlinear dynamics.

Keywords
Amplitude control
Chaotic dynamics
Extreme events
Nonhyperbolic system
Parametric control
Piecewise linear nonlinearity
Funding
None.
Conflict of interest
Paul Didier Kamdem Kuate is an Editorial Board Member of this journal, but was not in any way involved in the editorial and peer-review process conducted for this paper, directly or indirectly. Separately, other authors declared that they have no known competing financial interests or personal relationships that could have influenced the work reported in this paper.
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