Noise-Induced Transitions in Nonlinear Oscillators: From Quasi-Periodic Stability to Stochastic Chaos

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Noise-Induced Transitions in Nonlinear Oscillators: From Quasi-Periodic Stability to Stochastic Chaos

Popis výsledku v původním jazyce

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 &amp; 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 &amp; 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.

Název v anglickém jazyce

Noise-Induced Transitions in Nonlinear Oscillators: From Quasi-Periodic Stability to Stochastic Chaos

Popis výsledku anglicky

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 &amp; 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 &amp; 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10300 - Physical sciences

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

Fractal and Fractional

ISSN

2504-3110

e-ISSN

2504-3110

Svazek periodika

9

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

43

Strana od-do

550

Kód UT WoS článku

001558284600001

EID výsledku v databázi Scopus

2-s2.0-105014497577