Abstract
An example of an autoparametric system with external excitation is considered. We investigate the stability of the semi-trivial solution, that is the solution corresponding to the case with a non-oscillating non-excited subsystem. It is found that autoparametric resonance stands when this semi-trivial solution becomes unstable. Within a certain interval of the excitation frequency, two locally stable solutions exist: the semi-trivial and the non-trivial. For a given stationary solution the presented method permits one to determine the domains of attraction of the above solutions for given disturbances.
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