Frequency analysis of parametrically controlled oscillating systems

Constant Switching Frequency Self-Oscillating Controlled Class-D Amplifiers

Parametrically amplified radiation in a cavity with an oscillating wall

We introduce a time-dependent perturbation method to calculate the number of created particles in a 1D cavity with an oscillating wall of the frequency Ω. This method makes it easy to find the dominant part of the solution which results from the parametric resonance. The maximal number of particles are created at the mode frequency Ω/2. Using the Floquet theory, we discuss the long-time behavio...

Sensitivity Analysis for Oscillating Dynamical Systems

Boundary value formulations are presented for exact and efficient sensitivity analysis, with respect to model parameters and initial conditions, of different classes of oscillating systems. Methods for the computation of sensitivities of derived quantities of oscillations such as period, amplitude and different types of phases are first developed for limit-cycle oscillators. In particular, a no...

NORMAL FORM SOLUTION OF REDUCED ORDER OSCILLATING SYSTEMS

This paper describes a preliminary investigation into the use of normal form theory for modelling large non-linear dynamical systems. Limit cycle oscillations are determined for simple two-degree-of-freedom double pendulum systems. The double pendulum system is reduced into its centre manifold before computing normal forms. Normal forms are obtained using a period averaging method which is appl...

Quasipatterns in parametrically forced systems.

We examine two mechanisms that have been put forward to explain the selection of quasipatterns in single- and multifrequency forced Faraday wave experiments. Both mechanisms can be used to generate stable quasipatterns in a parametrically forced partial differential equation that shares some characteristics of the Faraday wave experiment. One mechanism, which is robust and works with single-fre...