A systematic framework for classification of parameter space dynamics in the Duffing oscillator

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F25%3A10258860" target="_blank" >RIV/61989100:27740/25:10258860 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S259012302503909X" target="_blank" >https://www.sciencedirect.com/science/article/pii/S259012302503909X</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.rineng.2025.107857" target="_blank" >10.1016/j.rineng.2025.107857</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A systematic framework for classification of parameter space dynamics in the Duffing oscillator

Popis výsledku v původním jazyce

This paper introduces a systematic framework for classifying the parameter space of the Duffing oscillator into three distinct levels. The first level categorizes the parameter space based on statistical properties, identifying diverging, non-diverging, and fixed point attractors. The second level focuses on the nature of the eigenvalues. In this paper, nine distinct types and their corresponding parameter ranges are identified. Finally, the third level classifies chaotic and periodic behaviors using Lyapunov exponents. For a single initial state, 19965 cases are analyzed, revealing that most of the parameter space is diverging, with few regions of nondiverging cases, highlighting the importance of precise design decisions to remain in stable regions. With the variation in initial states, the category distribution also varies across the parameter space. To this end, the analysis of selected cases from classification results is conducted using tools: attractors, multistability, time series, Lyapunov exponents, binary mapping, return map, Poincar &amp; eacute; map, and power spectrum. In addition, the representation of behavior across classified parameter space is obtained. Moreover, the design choices made to replicate the behavior of the Duffing oscillator in its electrical circuit counterpart are presented, ensuring alignment in their dynamic responses. Hardware experiments validated the chaotic and periodic behaviors under varying conditions. The comprehensive dataset including attractors, Lyapunov exponents, and categorized parameter space is created that can be used in the future and offers a valuable resource for engineers and researchers.

Název v anglickém jazyce

A systematic framework for classification of parameter space dynamics in the Duffing oscillator

Popis výsledku anglicky

This paper introduces a systematic framework for classifying the parameter space of the Duffing oscillator into three distinct levels. The first level categorizes the parameter space based on statistical properties, identifying diverging, non-diverging, and fixed point attractors. The second level focuses on the nature of the eigenvalues. In this paper, nine distinct types and their corresponding parameter ranges are identified. Finally, the third level classifies chaotic and periodic behaviors using Lyapunov exponents. For a single initial state, 19965 cases are analyzed, revealing that most of the parameter space is diverging, with few regions of nondiverging cases, highlighting the importance of precise design decisions to remain in stable regions. With the variation in initial states, the category distribution also varies across the parameter space. To this end, the analysis of selected cases from classification results is conducted using tools: attractors, multistability, time series, Lyapunov exponents, binary mapping, return map, Poincar &amp; eacute; map, and power spectrum. In addition, the representation of behavior across classified parameter space is obtained. Moreover, the design choices made to replicate the behavior of the Duffing oscillator in its electrical circuit counterpart are presented, ensuring alignment in their dynamic responses. Hardware experiments validated the chaotic and periodic behaviors under varying conditions. The comprehensive dataset including attractors, Lyapunov exponents, and categorized parameter space is created that can be used in the future and offers a valuable resource for engineers and researchers.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

—

Návaznosti

O - Projekt operacniho programu

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Results in Engineering

ISSN

2590-1230

e-ISSN

2590-1230

Svazek periodika

28

Číslo periodika v rámci svazku

December

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

22

Strana od-do

107857

Kód UT WoS článku

001606410600002

EID výsledku v databázi Scopus

2-s2.0-105020577658