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ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

Stochastic Global Dynamics of a Duffing Oscillator with a Symmetry-Breaking Parameter

Journal of Vibration Testing and System Dynamics 9(2) (2025) 169--177 | DOI:10.5890/JVTSD.2025.06.007

Kaio C. B. Benedetti$^{1}$, Paulo B. Gon\c{c}alves$^{2}$, Stefano Lenci$^{3}$, Giuseppe Rega$^{4}$

$^{1}$ School of Civil and Environmental Engineering, Federal University of Goi'{a}s, Goi^{a}nia, Brazil

$^{2}$ Department of Civil and Environmental Engineering, Pontifical Catholic University of Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil

$^{3}$ Department of Civil and Building Engineering, and Architecture, Polytechnic University of Marche, Ancona, Italy

$^{4}$ Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Italy

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Abstract

The symmetric Duffing oscillator is well studied in literature and may describe a plethora of events in sciences and engineering, including systems with one or two potential wells. However, in many applications ranging from quantum physics to engineering, a symmetry-breaking effect described by a quadratic nonlinear term is an important feature, and the magnitude of the quadratic term is often unknown. Here the influence of a nondeterministic quadratic term on the global dynamics of a Duffing oscillator with a double potential well is investigated. To this end, the Adaptative Ulam Method is employed, refining the complex basins' boundaries and allowing the analysis of nondeterministic effects. Depending on the forcing magnitude and frequency, the system may exhibit intra or cross-well periodic, quasi-periodic, or chaotic motions.

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