Variational iteration method has been favourably applied to various kinds of nonlinear problems. The main property of the method is in its flexibility and ability to solve nonlinear equations accurately and conveniently. In this paper recent trends and developments in the use of the method are reviewed. Major applications to nonlinear wave equation, nonlinear fractional differential equations, ...

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...

tailed discussion and analysis of the start-up and steady-state oscillation conditions for transistor LC oscillators with emphasis on CMOS devices. Part II presents both linear and nonlinear phase noise models for the parallel feedback and negative resistance oscillators. Each approach to the oscillator phase noise calculation has its own advantages and drawbacks. For example, the linear Leeson...

In this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the Maclaurin series of the exact solution. Nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. These equations equip a significant mathematical model for dynamical systems. The accuracy o...

Abstract The Gaylord's oscillator is a vibrating of uniform rigid rod without slipping on circular surface with definite radius. dominant equation motion was the outcome strongly nonlinear pendulum second order. run article interested in obtaining frequency–amplitude and approximate solution by simpler approach. relationship derived terms Bessel function. Quasi-exact periodic depends non-pertur...

Beyond the rotating-wave approximation, the dynamics of a quantum oscillator interacting strongly and off-resonantly with a two-level system exhibit beatings, whose period equals the revival time of the two-level system. On a longer time scale, the quantum oscillator shows collapses, revivals and fractional revivals, which are encountered in oscillator observables like the mean number of oscill...

The interaction of a quantum deformed oscillator with the environment is studied deriving a master equation whose form strongly depends on the type of deformation. PACS number(s): 03.70.+k, 02.50.-r Quantum groups [1] introduced as a mathematical description of deformed Lie algebras have given the possibility to generalize the notion of creation and annihiliation operators of the usual oscillat...

The nonlinear Schrödinger equation with general nonlinearity of polynomial growth and harmonic confining potential is considered. More precisely, the confining potential is strongly anisotropic; i.e., the trap frequencies in different directions are of different orders of magnitude. The limit as the ratio of trap frequencies tends to zero is carried out. A concentration of mass on the ground st...