Dynamics of non-autonomous oscillator with a controlled phase and frequency of external forcing

•Dynamics of a non-autonomous oscillator with adaptive properties, when the phase and frequency of the external force depend on the dynamical variable is studied.•Occurrence of chaotic dynamics in both models is observed.•Investigation of various parameter plane of external forcing was carried out.•Features of chaotic signal generating by the non-autonomous oscillator with analysis of Fourier spectra and phase portraits is studied.•Comparative analysis numerical results and physical experiment is presented. The dynamics of a non-autonomous oscillator in which the phase and frequency of the external force depend on the dynamical variable is studied. Such a control of the phase and frequency of the external force leads to the appearance of complex chaotic dynamics in the behavior of oscillator. A hierarchy of various periodic and chaotic oscillations is observed. The structure of the space of control parameters is studied. It is shown there are oscillatory modes similar to those of a non-autonomous oscillator with a potential in the form of a periodic function in the system dynamics, but there are also significant differences. Physical experiments of such systems are implemented.