Robustness of a relaxation oscillator

Robustness of a relaxation oscillator

For a relaxation oscillator which consists of a relay-hysteresis in feedback with negative integral action we prove that the oscillatory behaviour is robust to perturbations in the dynamical component of the feedback loop which are sufficiently small in a gap sense.

Tracking Rhythms with a Relaxation Oscillator

Finding downbeats with a relaxation oscillator.

A relaxation oscillator model of neural spiking dynamics is applied to the task of finding downbeats in rhythmical patterns. The importance of downbeat discovery or 'beat induction' is discussed, and the relaxation oscillator model is compared to other oscillator models. In a set of computer simulations the model is tested on 35 rhythmical patterns. The model performs well, making good predicti...

Relaxation of a qubit measured by a driven Duffing oscillator

I. Serban,1,2,3 M. I. Dykman,4,* and F. K. Wilhelm1,† 1IQC and Deptartment of Physics and Astronomy, University of Waterloo, 200 University Avenue W, Waterloo, Ontario N2L 3G1, Canada 2Department Physik, Arnold-Sommerfeld-Center for Theoretical Physics, and Center for Nanoscience, Ludwig-Maximilians-Universität, Theresienstrasse 37, D-80333 München, Germany 3Instituut Lorentz, Leiden University...

Scaling in Singular Perturbation Problems: Blowing Up a Relaxation Oscillator

An introduction to some recently developed methods for the analysis of systems of singularly perturbed ordinary differential equations is given in the context of a specific problem describing glycolytic oscillations. In suitably scaled variables the governing equations are a planar system of ordinary differential equations depending singularly on two small parameters ε and δ. In [20] it was arg...