The cathode-coupled oscillator as a quasi-linear system

A Damped Oscillator as a Hamiltonian System

1 Problem It is generally considered that systems with friction are not part of Hamiltonian dynamics, but this is not always the case. Show that a (nonrelativistic) damped harmonic oscillator can be described by a Hamiltonian (and by a Lagrangian), with the implication that Liouville's theorem applies here. Consider motion in coordinate x of a particle of mass m with equation of motion, m¨x + β...

A Quasi-linear Parabolic System of Chemotaxis

We consider a quasi-linear parabolic system with respect to unknown functions u and v on a bounded domain of n-dimensional Euclidean space. We assume that the diffusion coefficient of u is a positive smooth function A(u), and that the diffusion coefficient of v is a positive constant. If A(u) is a positive constant, the system is referred to as socalled Keller-Segel system. In the case where th...

Diverse routes to oscillation death in a coupled oscillator system.

We study oscillation death (OD) in a well-known coupled-oscillator system that has been used to model cardiovascular phenomena. We derive exact analytic conditions that allow the prediction of OD through the two known bifurcation routes, in the same model, and for different numbers of coupled oscillators. Our exact analytic results enable us to generalize OD as a multiparameter-sensitive phenom...

Learning of Spatio-Temporal Codes in a Coupled Oscillator System

In this paper, we consider a learning strategy that allows one to transmit information between two coupled phase oscillator systems (called teaching and learning systems) via frequency adaptation. The dynamics of these systems can be modeled with reference to a number of partially synchronized cluster states and transitions between them. Forcing the teaching system by steady but spatially nonho...

State-dependent impedance of a strongly coupled oscillator-qubit system