The conventional quantization of the harmonic oscillator in terms of operators Q and P can be implemented with the help of irreducible unitary representations of the Heisenberg-Weyl group which acts transitively and effectively on the simply connected classical phase space Sq,p ∼= R . In the description of the harmonic oscillator in terms of angle and action variables φ and I the associated pha...

By introducing Colpitts oscillator as a chaotic system, this paper deals with back-stepping control method and investigates the restrictions and problems of the controller where non-existence of a suitable response in the presence of uncertainty is the most important problem to note. In this paper, the back-stepping sliding mode method is introduced as a robust method for controlling nonlinear ...

the dynamical behaviour of the forced escape oscillator, which depends on the parameter values we considered, have been studied numerically using the techniques of phase portraits and poincar'{e} sections. also, we employed perturbation methods such as lindstedt's method to obtain the frequency-amplitude relation of escape oscillator.

We show that information on the probability density of local fluctuations can be obtained from a numerical renormalization group calculation of a reduced density matrix. We apply this approach to the Anderson-Holstein impurity model to calculate the ground state probability density ρ(x) for the displacement x of the local oscillator. From this density we can deduce an effective local potential ...

The cutting sound in the audible range includes plenty of tool wear information. The sound is sampled by the acoustic emission AE sensor as a short-time sequence, then worn wear can be detected by the Duffing-Holmes oscillator. A novel engineering method is proposed for determining the chaotic threshold of the Duffing-Holmes oscillator. First, a rough threshold value is calculated by local Lyap...

Cλ-extended oscillator algebras generalizing the Calogero-Vasiliev algebra, where Cλ is the cyclic group of order λ, are studied both from mathematical and applied viewpoints. Casimir operators of the algebras are obtained, and used to provide a complete classification of their unitary irreducible representations under the assumption that the number operator spectrum is nondegenerate. Deformed ...

We analyze conditions under which the precision of coupled oscillators can be improved by synchronization. The improvement in precision, defined as the inverse of the coefficient of variation of the periods, depends on how noise is added to the system. If the magnitude of noise experienced by an oscillator only depends on the state of that oscillator, then the precision of the group rhythm can ...

A coupled-oscillators-model-based method for measuring speech rhythm is presented. This model explains crosslinguistic differences in rhythm as deriving from varying degrees of coupling strength between a syllable oscillator and a phrase stress oscillator. The method was applied to three texts read aloud in French, in Brazilian and European Portuguese by seven speakers. The results reproduce th...