Cλ-extended oscillator algebras, where Cλ is the cyclic group of order λ, are introduced and realized as generalized deformed oscillator algebras. For λ = 2, they reduce to the well-known Calogero–Vasiliev algebra. For higher λ values, they are shown to provide in their bosonic Fock space representation some interesting applications to supersymmetric quantum mechanics and some variants thereof:...

An ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses shows a range of non-trivial behavior, from synchronization, desynchronization, to clustering. The group behavior that arises in the ensemble can be predicted from the phase response of a single oscillator to a given impulsive perturbation. We present a theory based on phase reduction of a jump stochastic process...

A differential calculus is set up on a deformation of the oscillator algebra. It is uniquely determined by the requirement of invariance under a seven-dimensional quantum group. The quantum space and its associated differential calculus are also shown to be invariant under a nine generator quantum group containing the

In this paper we present a 2μW temperature compensated on-chip digitally controlled oscillator and a 70nW uncompensated, ultra low power oscillator. The temperature compensated oscillator has a temperature stability of 8ppm/C while uncompensated oscillator has a stability of 4%/C. The uncompensated oscillator is calibrated using stable oscillator often to achieve high effective temperature stab...

We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For [Formula: see text] oscillators, there are four possible types of attractors: completely synchronized fixed poin...

Accurate detection of weak periodic signals within noise and possibility of secure messaging have made Duffing oscillator (DO) highly important in the field of communication. Investigation on the properties of DO is thus ardently sought for. An elegant approach to accomplish the same is to fabricate electronic circuit simulating DO non-linear equation and to study the effect of input signal amp...

While internal space-time symmetries of relativistic particles are dictated by the little groups of the Poincaré group, it is possible to construct representations of the little group for massive particles starting from harmonic oscillator wave functions for the quark model. The resulting oscillator wave functions are covariant and can be Lorentz-boosted. It is thus possible to obtain the parto...