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Sergei Glebov

Publications and source records attributed to Sergei Glebov.

6 recordsLinked to original sources
arXiv2010

Forced Nonlinear Resonance in a System of Coupled Oscillators

We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time $t \sim ε^{-2}$ one component of the system is described in the main by the inhomogeneous Mathieu equation while the other component represents pulsation of large amplitude. A Hamiltonian system is obtained which describes the behaviour of the envelope in the main. The analytic results agree to numerical simulations.

math-ph↗
arXiv2009

Autoresonance in a Dissipative System

We study the autoresonant solution of Duffing's equation in the presence of dissipation. This solution is proved to be an attracting set. We evaluate the maximal amplitude of the autoresonant solution and the time of transition from autoresonant growth of the amplitude to the mode of fast oscillations. Analytical results are illustrated by numerical simulations.

math-ph↗
arXiv2009

Autoresonant germ in dissipative system

We study an initial stage of autoresonant growth of a solution in a dissipative system. We construct an asymptotic formula of an autoresonant germ that is an attractor for autoresonant solutions. We present a moment of a fall and a maximum value of the amplitude for the germ. Numerical simulations are done.

math-ph↗
arXiv2007

The autoresonance threshold into a system of weakly coupled oscillators

We investigate a system of two weakly coupled oscillators. It is shown that an external periodic perturbation can lead to the capture into resonance. Asymptotic description and numerical simulations are presented. We have obtained the explicit formula for the threshold value for the amplitude of the perturbation that leads to the autoresonance.

math-ph↗
arXiv2005

Finite amplitude waves under a small resonant driving force

We construct a special asymptotic solution for the forced Boussinesq equation. The perturbation is small and oscillates with a slowly varied frequency. The slow passage through the resonance generates waves with the finite amplitude. This phenomenon is described in details.

nlin.PS↗