We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1 : 1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to obtain the frequencyamplitude modulat...

The driven nonlinear Duffing oscillator is a very good, and standard, example of a quantum mechanical system from which classical-like orbits can be recovered from unravelings of the master equation. In order to generate such trajectories in the phase space of this oscillator, in this paper we use the quantum jump unraveling together with a suitable application of the correspondence principle. ...

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...

We present an analytical calculation of the response a driven Duffing oscillator to low-frequency fluctuations in resonance frequency and damping. find that these parameters manifest themselves distinctively, allowing them be distinguished. In strongly nonlinear regime, amplitude phase noise due damping are attenuated, while transduction into remains order $1$. show this can seen by comparing r...

in the present paper the behavior of an elastically mounted cylinder in low and high mass-damping ratio is investigated. for high mass-damping ratio, a classical wake oscillator model is used. at the first, by neglecting all damping and nonlinear terms of this model, the possibility of using a linear model for determination of the lock-in range and the dominant mode is investigated. then, witho...

We study analytically and numerically the noise-induced transition between an absorbing and an oscillatory state in a Duffing oscillator subject to multiplicative, Gaussian white noise. We show in a non-perturbative manner that a stochastic bifurcation occurs when the Lyapunov exponent of the linearised system becomes positive. We deduce from a simple formula for the Lyapunov exponent the phase...

Abstract This paper investigates the dynamics of a Duffing oscillator excited by an unbalanced motor. The interaction between motor and vibrating system is considered as nonideal, which means that excitation provided can be influenced response, case in general for real systems. constitutes important difference with respect to classical (ideally excited) oscillator, where amplitude frequency ext...

The paper proposes an alternative approach to emotion recognition from stimulated EEG signals using Duffing oscillator. Reported works on emotion clustering generally employ the principles of supervised learning. Unfortunately, because of noisy and limited feature set, the classification problem often suffers from high inaccuracy. This has been overcome in this paper by submitting the EEG signa...