Nonlinear elastic effects play an important role in the dynamics of microelectromechanical systems (MEMS). A Duffing oscillator is widely used as an archetypical model of mechanical resonators with nonlinear elastic behavior. In contrast, nonlinear dissipation effects in micromechanical oscillators are often overlooked. In this work, we consider a doubly clamped micromechanical beam oscillator,...

This paper investigates the design and analysis of a novel energy harvesting device that uses magnetic levitation to produce an oscillator with a tunable resonance. The governing equations for the mechanical and electrical domains are derived to show the designed system reduces to the form of a Duffing oscillator under both static and dynamic loads. Thus, nonlinear analyses are required to inve...

The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relat...

A two-dimensional Duffing oscillator which can produce stochastic resonance (SR) is studied in this paper. We introduce its SR mechanism and present a generalized parameter-adjusted SR (GPASR) model of this oscillator for the necessity of parameter adjustments. The Kramers rate is chosen as the theoretical basis to establish a judgmental function for judging the occurrence of SR in this model; ...

Using the decoherence formalism of Gell-Mann and Hartle, a quantum system is found which is the equivalent of the classical dissipative chaotic Duffing oscillator. The similarities and differences from the classical oscillator are examined; in particular, a new concept of quantum maps is introduced, and alterations in the classical strange attractor due to the presence of scale-dependent quantu...

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. ...

<p style='text-indent:20px;'>This paper analyzes conservation issues in the discretization of certain stochastic dynamical systems by means <inline-formula><tex-math id="M2">\begin{document}$ \vartheta $\end{document}</tex-math></inline-formula>-mehods. The analysis also takes into account effects estimation expected values Monte Carlo simulations. theoretical is s...

The chaotic synchronization regime in coupled dynamical systems is considered. It has been shown that the onset of a synchronous regime is based on the appearance of a phase relation between the interacting chaotic oscillator frequency components of Fourier spectra. The criterion of synchronization of spectral components as well as the measure of synchronization has been discussed. The universa...

The problem of hybrid chaos synchronization is investigated, where a digital response subsystem is designed to synchronize with an analog drive subsystem. The approach taken is a new prediction-based digital redesign for a continuous-time observer embedded in the response via an optimal linearization approach of the nonlinear chaotic systems. Three typical but topologically quite different chao...