Abstract This is a demonstration of the PNLSS Toolbox 1.0. The toolbox designed to identify polynomial nonlinear state-space models from data. Nonlinear can describe wide range systems. An illustration provided on experimental data an electrical system mimicking forced Duffing oscillator, and numerical fluid dynamics problem.

in this work, time domain analysis is used to solve adler’s equation in order to obtain the required time, for an oscillator under external injection, reaching the steady-state condition. mathematical approach has been applied to fully describe the transient of frequency acquisition in injection-locked lc and ring oscillators considering their time-varying nature. then, the analysis is verified...

Nonlinear dynamics of the magnetic vortex state in a circular nanodisk was studied under a perpendicular alternating magnetic field that excites the radial modes of the magnetic resonance. Here, we show that as the oscillating frequency is swept down from a frequency higher than the eigenfrequency, the amplitude of the radial mode is almost doubled to the amplitude at the fixed resonance freque...

The effect of stochastic perturbations on nearly homoclinic pulse trains is considered for three model systems: a Duffing oscillator, the Lorenz-like Shimizu-Morioka model, and a co-dimension-three normal form. Using the Duffing model as an example, it is demonstrated that the main effect of noise does not originate from the neighbourhood of the fixed point, as is commonly assumed, but due to t...

A new class of time-integrators is presented for strongly nonlinear dynamical systems. These algorithms are far superior to the currently common time integrators in computational efficiency and accuracy. These three algorithms are based on a local variational iteration method applied over a finite interval of time. By using Chebyshev polynomials as trial functions andDirac–Delta functions as th...

Accurately predicting the onset of large behavioral deviations associated with saddlenode bifurcations is imperative in a broad range of sciences and for a wide variety of purposes, including ecological assessment, signal amplification, and microscale mass sensing. In many such practices, noise and non-stationarity are unavoidable and everpresent influences. As a result, it is critical to simul...

We derive the exact bifurcation diagram of the Duffing oscillator with parametric noise thanks to the analytical study of the associated Lyapunov exponent. When the fixed point is unstable for the underlying deterministic dynamics, we show that the system undergoes a noise-induced reentrant transition in a given range of parameters. The fixed point is stabilised when the amplitude of the noise ...

In the present study, several successive approximate solutions of nonlinear oscillator are derived by using efficient frequency formula. A systematical analysis formulation helps to establish a general periodic solution. Each approximation represents, individually, solution oscillator. For optimal design and accurate prediction structural behavior, new optimizer is demonstrated for solutions. T...

Periodically driven oscillators are commonly described in a frame corotating with the drive and using rotating-wave approximation (RWA). This description, however, is known to induce errors for off-resonant driving. Here, we show that standard quantum creation annihilation of particles oscillators' natural frequency, necessarily leads incorrect results when combined RWA. We demonstrate this on ...

The bifurcation structure of coupled periodically driven double-well Duffing oscillators is investigated as a function of the strength of the driving force f and its frequency Ω. We first examine the stability of the steady state in linear response, and classify the different types of bifurcation likely to occur in this model. We then explore the complex behaviour associated with these bifurcat...