– We consider a population of parametrically excited globally coupled oscillators in a weakly nonlinear state. The instabilities of collective modes lead to a traveling-wave regime, where intensities of oscillations of each oscillator vary periodically in time. For large excitation amplitudes a frozen state with nearly uniform oscillation intensities is observed. Ensembles of coupled oscillator...

This paper discusses a novel technique and implementation to perform nonlinear control for two different forced model state oscillators and actuators. The paper starts by discussing the Duffing oscillator which features a second order non-linear differential equation describing complex motion whereas the second model is the Van der Pol oscillator with non-linear damping. A first order actuator ...

Analysis of the Super Saw was done in order to provide a detailed understanding of this special oscillator found in the Roland JP-8000 and JP-8080. There are currently no software synthesizers available which have the Super Saw oscillator or any faithful recreations which could represent this special oscillator. With the results and findings in this thesis, it will be possible to emulate the Su...

Circadian clocks are biochemical oscillators that allow organisms to estimate the time of the day. These oscillators are inherently noisy due to the discrete nature of the reactants and the stochastic character of their interactions. To keep these oscillators in sync with the daily day-night rhythm in the presence of noise, circadian clocks must be coupled to the dark-light cycle. In this manus...

In addition to the passive observation of a non­ linear oscillator and the description of the measured data with Lyapounow exponents [1, 2], fractal dimensions [3-5], entropies [6], etc. it is possible to charcterize a non-linear oscillator by an active method, namely by determining its response to specific perturbations. The resonances of harmonic systems which are brought about by a sinusoida...

For most practical purposes, the focus is often on obtaining statistical moments of the response of stochastically driven oscillators than on the determination of pathwise response histories. In the absence of analytical solutions of most nonlinear and higherdimensional systems, Monte Carlo simulations with the aid of direct numerical integration remain the only viable route to estimate the sta...