duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. this paper presents he´s energy balance method (ebm) for solving nonlinear differential equations. two strong nonlinear cases have been studied analytically. analytical results of the ebm are compared with the solutions obtained by using he´s frequency amplitude formulation (faf) and numerical solu...

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 analyze the co-normally induced quasiregular representation for two families of Lie groups: the 2d-oscillator groups N!SO(2d) where N is the free two-step nilpotent group on 2d generators, and the dilated 2d-oscillator groups N ! (SO(2d)× R+). We construct irreducible decompositions in both cases with explicit spectrum and intertwining operators, and in both cases we prove a Caldéron-type ad...

Two new types of coherent states associated with the Cλ-extended oscillator, where Cλ is the cyclic group of order λ, are introduced. They satisfy a unity resolution relation in the Cλ-extended oscillator Fock space (or in some subspace thereof) and give rise to Bargmann representations of the latter, wherein the generators of the Cλ-extended oscillator algebra are realized as differential-oper...

Abstract. A finite oscillator dictionary which has important applications in sequences designs and the compressive sensing was introduced by Gurevich, Hadani and Sochen. In this paper, we first revisit closed formulae of the finite split oscillator dictionary S by a simple proof. Then we study the non-split tori of the group SL(2, Fp). Finally, An explicit algorithm for computing the finite non...

 In this work, time domain analysis is used to solve Adler’s equation in order to obtain the required time, for an oscillator under external injection, reaching the steady-state condition. Mathematical approach has been applied to fully describe the transient of frequency acquisition in injection-locked LC and Ring oscillators considering their time-varying nature. Then, the analysis is verifie...

We classify all genuine unitary representations of the metaplectic group whose infinitesimal character is real and at least as regular as that of the oscillator representation. In a previous paper we exhibited a certain family of representations satisfying these conditions, obtained by cohomological induction from the tensor product of a one-dimensional representation and an oscillator represen...