In this paper, the nonlinear dynamics of a non-autonomous system model for third order sub-harmonic in a basic ferroresonant circuit are analyzed in details, including phase trajectory, Poincaré map, bifurcation diagram, dissipativity analysis and Spectrogram map. Furthermore, a sliding mode controller of the system is designed and both theory analysis and numerical simulation are presented, wh...

This paper reports on the stability analysis of one member of a dual-channel resonant dc–dc converter family. The study is confined to the buck configuration in symmetrical operation. The output voltage of the converter is controlled by a closed loop applying constant-frequency pulsewidth modulation. The dynamic analysis reveals that a bifurcation cascade develops as a result of increasing the ...

the aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. in [1], ungar and chen showed that the algebra of the group sl(2,c) naturally leads to the notion of gyrogroups and gyrovector spaces for dealing with the lorentz group and its underlying hyperbolic geometry. they defined the chen addition and then chen model of hyperbolic geometry. in this paper,...

we obtain 1.1 ([4], [14]). The aim of this paper is to give some results concerning the so called Poincaré Problem. Roughly speaking, this problem asks for a numerical criteria to identify when a morphism F : L −→ TS, defining a foliation, is equal to another of the form Tf −→ TS, with f : S −→ P 1 a holomorphic map and Tf (that must be isomorphic to our original L) the sheaf of relative vector...

Dynamical properties of the two limit cycles in a ultradiscrete Sel'kov model are analytically investigated. We construct Poincaré map for and reveal their stabilities; one is attracting other repelling. Basins identified. It found that basin repelling cycle has self-similar structure. also review from viewpoint integrable system theory.

The goal of our work is to give a complete fractal classification planar analytic nilpotent singularities. For the classification, we use notion box dimension (two-dimensional) orbits on separatrices generated by unit time map. We also show how one-dimensional orbit Poincaré map, defined characteristic curve near center/focus, reveals an upper bound for number limit cycles singularity. introduc...

Open flows over a cavity present, even at medium Reynolds number, sustained oscillations resulting from a complex feedback process [1]. Previous works have reveals a mode-switching phenomenon which remains to characterize from a dynamical point of view. In the configuration here investigated, the intermittency between the two dominant modes is characterized using a symbolic dynamics based appro...

A new singular perturbation method based on the Lie symmetry group is presented to a system of difference equations. This method yields consistent derivation of a renormalization group equation which gives an asymptotic solution of the difference equation. The renormalization group equation is a Lie differential equation of a Lie group which leaves the system approximately invariant. For a 2-D ...

1. We consider differential topology to be the study of differentiable manifolds and differentiable maps. Then, naturally, manifolds are considered equivalent if they are diffeomorphic, i.e., there exists a differentiable map from one to the other with a differentiable inverse. For convenience, differentiable means C; in the problems we consider, C' would serve as well. The notions of different...