The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, ...

We study the impulsive responses of a grounded linear oscillator coupled to a light nonlinear attachment through an essentially nonlinear (nonlinearizable) stiffness. We analyze the periodic and quasi-periodic dynamics of the undamped system forced by a single impulse on the linear oscillator and being initially at rest, by considering separately low-, moderateand high-energy impulsive motions....

Vibrations of a nonlinear oscillator with an attached pendulum, excited by movement of its point of suspension, have been analysed in the paper. The derived differential equations of motion show that the system is strongly nonlinear and the motions of both subsystems, the pendulum and the oscillator, are strongly coupled by inertial terms, leading to the so-called autoparametric vibrations. It ...

We study some basic quantum confinement effects through investigation a deformed harmonic oscillator algebra. We show that spatial confinement effects on a quantum harmonic oscillator can be represented by a deformation function within the framework of nonlinear coherent states theory. Using the deformed algebra, we construct a quantum field theory in confined space. In particular, we find that...

A higher-order oscillator, including a nonlinear unit and an 8th-order low-pass active Bessel ̄lter is described. The Bessel unit plays the role of \three-in-one": a delay line, an ampli ̄er and a ̄lter. Results of hardware experiments and numerical simulation are presented. Depending on the parameters of the nonlinear unit the oscillator operates either in a one-scroll or two-scroll mode. Two pos...

Inclusion of the instantaneous Kerr nonlinearity in the FDTD framework leads to implicit equations that have to be solved iteratively. In principle, explicit integration can be achieved with the use of anharmonic oscillator equations, but it tends to be unstable and inappropriate for studying strong-field phenomena like laser filamentation. In this paper, we show that nonlinear susceptibility c...

We investigate a simple variation of the series RLC circuit in which anti-parallel diodes replace the resistor. This results in a damped harmonic oscillator with a nonlinear damping term that is maximal at zero current and decreases with an inverse current relation for currents far from zero. A set of nonlinear differential equations for the oscillator circuit is derived and integrated numerica...

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...

Hassan Khalil’s research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building blocks in digital systems. The paper first investigates local and global stability proper...

2. COUPLED OSCILLATOR USING TRANSCONDUCTORS A CMOS neural oscillator using negative resistance has An ideal coupled oscillator using two operational been designed and fabricated in an AMI O S u m double transconductace amplifiers (OTAs) and two capacitors is poly technology through MOSIS. The proposed neural shown in Fig. 1. oscillator consists of a nonlinear resistor with negative resistance a...