In this paper we study to what extent the canonical equivalence and the identity of the geometric phases of dissipative and conservative linear oscillators, established in a preceeding paper, can be generalized to nonlinear ones. Considering first the 1-D quartic generalized oscillator we determine, by means of a perturbative time dependent technic of reduction to normal forms, the canonical tr...

We propose an analog current-mode subthreshold CMOS circuit implementing a piecewise linear neuromorphic oscillator. Our circuit was derived from a piecewise linear oscillator model proposed by Matsuoka, well known as a building block for constructing a robot locomotion controller. We modified Matsuoka’s oscillator to be suitable for analog current-mode integrated circuit implementation, and de...

The linearly damped oscillator equation is considered with the damping term generalized to a Caputo fractional derivative. The order of the derivative being considered is 0 ≤ v ≤ 1. At the lower end v 0 the equation represents an undamped oscillator and at the upper end v 1 the ordinary linearly damped oscillator equation is recovered. A solution is found analytically, and a comparison with the...

We define the “maximally integrable” isotropic oscillator on I CP and discuss its various properties, in particular, the behaviour of the system with respect to a constant magnetic field. We show that the properties of the oscillator on I CP qualitatively differ in the N > 1 and N = 1 cases. In the former case we construct the “axially symmetric” system which is locally equivalent to the oscill...

The generalized Duffin-Kemmer-Petiau (DKP) oscillator with electromagnetic interactions in the curved space-times are investigated. We introduce firstly DKP Som-Raychaudhuri space-time Cornell potential. Then, we consider into oscillator. energy eigenvalues and eigenfunction of our problem obtained. effect from parameters space-time, frequency oscillator, potential magnetic flux on have been an...

The semiclassical treatment of the two-dimensional harmonic oscillator provides an instructive example of the relation between classical motion and the quantum mechanical energy spectrum. We extend previous work on the anisotropic oscillator with incommensurate frequencies and the isotropic oscillator to the case with commensurate frequencies for which the Lissajous curves appear as classical p...