Self-Modulating Quasi-Regular and Chaotic Oscillations in a Nonlinear System of Two Connected Oscillators

Self-modulating and chaotic oscillations in a system of two coupled oscillators excited by an external periodic force are considered. It is assumed that the first oscillator has cubic nonlinearity and is connected to the second oscillator by a quadratic coupling. Two examples of problems leading to such a model are given: the first task is the task of exciting powerful hypersound in a ferrite plate with magnetically elastic properties; the second is the task of exciting electromagnetic noise vibrations in a ferrite disk placed in an electrodynamic resonator. It is noted that both problems can be reduced to solving a simplified system of two shortened oscillatory type equations, the first of which corresponds to a magnetic oscillator, and the second to an elastic or electrodynamic one. Time-based oscillation scans, parametric portraits for the displacement and its derivative, as well as frequency spectra of excited oscillations in a wide range of excitation amplitude are obtained. Two main oscillation modes have been identified: mode No. 1 — multiharmonic regularized, mode No. 2 — multiharmonic quasi–chaotic, which, starting from regular, alternately replace each other as the level of excitation increases.