Устойчивые и неустойчивые динамические процессы в автоколебательной системе с тремя степенями свободы

Abstract

The work is devoted to the study of the dynamic instability of coherent regimes of a system of two self-oscillators with a strong mutual resonant coupling. It is shown that this system can generate synchronous oscillations at three different frequencies, they correspond to the basic types of oscillations-modes: one in-phase and two anti-phase. A qualitative analysis of the influence of the characteristics of the resonant coupling on the stability of natural synchronous modes of oscillations has been carried out. An analytical criterion for the instability of in-phase oscillations and the conditions for its fulfillment are considered. The possibility of suppressing the stability of antiphase oscillations is discussed. The method of numerical simulation was used to study the temporal and spectral characteristics of oscillatory processes in various modes, including chaotic. Variants of the system behavior under competition and mode suppression accompanied by self-modulation processes are demonstrated. The features of dynamic chaos tuning and diagnostics of its components are discussed. The possibility of obtaining chaotic signals with a continuous spectrum in a band exceeding an octave is shown.