Noise-Induced Transitions in Nonlinear Oscillators: From Quasi-Periodic Stability to Stochastic Chaos
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F25%3A10258426" target="_blank" >RIV/61989100:27740/25:10258426 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2504-3110/9/8/550" target="_blank" >https://www.mdpi.com/2504-3110/9/8/550</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/fractalfract9080550" target="_blank" >10.3390/fractalfract9080550</a>
Alternative languages
Result language
angličtina
Original language name
Noise-Induced Transitions in Nonlinear Oscillators: From Quasi-Periodic Stability to Stochastic Chaos
Original language description
This paper presents a comprehensive dynamical analysis of a nonlinear oscillator subjected to both deterministic and stochastic excitations. Utilizing a diverse suite of analytical tools-including phase portraits, Poincar & eacute; sections, Lyapunov exponents, recurrence plots, Fokker-Planck equations, and sensitivity diagnostics-we investigate the transitions between quasi-periodicity, chaos, and stochastic disorder. The study reveals that quasi-periodic attractors exhibit robust topological structure under moderate noise but progressively disintegrate as stochastic intensity increases, leading to high-dimensional chaotic-like behavior. Recurrence quantification and Lyapunov spectra validate the transition from coherent dynamics to noise-dominated regimes. Poincar & eacute; maps and sensitivity analysis expose multistability and intricate basin geometries, while the Fokker-Planck formalism uncovers non-equilibrium steady states characterized by circulating probability currents. Together, these results provide a unified framework for understanding the geometry, statistics, and stability of noisy nonlinear systems. The findings have broad implications for systems ranging from mechanical oscillators to biological rhythms and offer a roadmap for future investigations into fractional dynamics, topological analysis, and data-driven modeling.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10300 - Physical sciences
Result continuities
Project
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Continuities
O - Projekt operacniho programu
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Fractal and Fractional
ISSN
2504-3110
e-ISSN
2504-3110
Volume of the periodical
9
Issue of the periodical within the volume
8
Country of publishing house
CH - SWITZERLAND
Number of pages
43
Pages from-to
550
UT code for WoS article
001558284600001
EID of the result in the Scopus database
2-s2.0-105014497577