Complex dynamics of a non-autonomous oscillator with a controlled phase of an external force

The dynamics of a non-autonomous oscillator in which the phase of external force linearly depends on a dynamic variable has been investigated. This control of the external-drive phase leads to the formation of a hierarchy of various periodic and chaotic oscillations. The structure of the space of control parameters has been studied. It is established that dynamics of the system exhibits oscillatory regimes analogous to those of a non-autonomous oscillator with potential in the form of a periodic function.