This article is cited in 4 papers

Nonlinear Systems

Oscillations and stability in quasiautonomous system. II. Critical point of the one-parameter family of periodic motions

V. N. Tkhai

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

Abstract: Consideration was given to the single-frequency oscillations of a periodic system allied to the nonlinear autonomous system. The publications of the present author demonstrated that the period on the family of oscillations of the autonomous system usually depends only on a single parameter. At that, the points of the family are divided into the ordinary (the derivative with respect to the period in parameter is other than zero) and critical (this derivative vanishes) points. Origination of oscillations at the critical point was studied. It was established that at least two resonance oscillations are generated. The first part of the paper considered the ordinary point.

Presented by the member of Editorial Board: L. B. Rapoport

Received: 17.02.2011

 English version: Automation and Remote Control, 2011, 72:7, 1450–1457

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