  The dynamics of magnetization and current-voltage characteristics of the
superconductor-ferromagnet-superconductor $\varphi_0$ Josephson junction in the
presence of external electromagnetic radiation have been studied. Effects of
radiation magnetic component are investigated in the frameworks of one- and
two-signal models. The implementation of two types of dynamical states of
magnetization is demonstrated. These states have a phase shift of $\pi$ in the
synchronization region of magnetic precession and Josephson oscillations and
differ in the nature of their time dependence. Transitions between these states
with increasing and decreasing bias current show hysteresis, which is reflected
in the bifurcation diagram and the current-voltage characteristics. We also
provide an experimental way to test the obtained results by measuring the phase
shift in voltage temporal dependence at fixed current value for both sweeping
directions. The results obtained can find application in various fields of
superconducting spintronics and quantum computing.
