Nonlinear Stochastic Dynamics of the Intermediate Dispersive Velocity Equation with Soliton Stability and Chaos

This paper examines the nonlinear behavior of the generalized stochastic intermediate dispersive velocity (SIdV) equation, which has been widely analyzed in a non-noise deterministic framework but has yet to be studied in any depth in the presence of varying forcing strength and noise types, in part...

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Veröffentlicht in:Entropy (Basel, Switzerland) Jg. 27; H. 11; S. 1176
Hauptverfasser: Wali, Samad, Munawar, Maham, Abdelkader, Atef, Jhangeer, Adil, Imran, Mudassar
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Switzerland MDPI AG 20.11.2025
Schlagworte:
basin stability
bifurcation diagram
Bifurcations
Control engineering
Differential equations
Electric power production
Energy harvesting
Fractals
Liapunov exponents
Lyapunov exponents
noise-induced chaos
Nonlinear dynamics
Oscillators
Power spectra
recurrence quantification
Signal processing
Solitary waves
Spectrum analysis
stochastic nonlinear dynamics
Systems stability
Germany
stochastic nonlinear dynamics
basin stability
Lyapunov exponents
noise-induced chaos
bifurcation diagram
recurrence quantification
ISSN:1099-4300, 1099-4300
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Zusammenfassung:This paper examines the nonlinear behavior of the generalized stochastic intermediate dispersive velocity (SIdV) equation, which has been widely analyzed in a non-noise deterministic framework but has yet to be studied in any depth in the presence of varying forcing strength and noise types, in particular how it switches between periodic, quasi-periodic, and chaotic regimes. A stochastic wave transformation reduces the equation to simpler ordinary differential equations to make soliton overlap analysis feasible to analyze soliton robustness under deterministic and stochastic conditions. Lyapunov exponents, power spectra, recurrence quantification, correlation dimension, entropy measures, return maps, and basin stability are then used to measure the effect of white, Brownian, and colored noise on attractor formation, system stability, and spectral correlations. Order–chaos transitions as well as noise-induced complexity are more effectively described by bifurcation diagrams and by Lyapunov spectra. The results of this experiment improve the theoretical knowledge of stochastic nonlinear waves and offer information that will be useful in the fields of control engineering, energy harvesting, optical communications, and signal processing applications.
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ISSN:1099-4300
1099-4300
DOI:10.3390/e27111176