The effect of the supersonic drift of charge carriers on phonon generation in tellurium crystals is studied under the conditions of the emergence of acoustic instability leading to dynamic chaos. All stages of the stochasticity evolution are traced experimentally with varying the external conditions, namely, the magnitude of the static electric field, determining the drift of charge carriers, and the magnitude and direction of the magnetic field. It is shown that with increasing electric and magnetic fields, the periodic oscillations of the current are transformed into random oscillations through the frequency-doubling and tripling bifurcations. A mathematical model in the form of phase trajectories of the dissipative dynamic system and the spectral portraits corresponding to transient processes are described.