  We report on unusual regimes of operation of a laser with a gain medium with
a large Raman scattering cross-section, which is often inherent in new types of
gain media such as colloidal and epitaxial quantum dots and perovskite
materials. These media are characterized by a strong electron-phonon coupling.
Using the Fr\"ohlich Hamiltonian to describe the electron-phonon coupling in
such media, we analyze the operation of the system above the lasing threshold.
We show that below a critical value of the Fr\"ohlich constant, the laser can
only operate in the conventional regime: namely, there are coherent cavity
photons but no coherent phonons. Above the critical value, a new pump rate
threshold appears. Above this threshold, either joint self-oscillations of
coherent phonons in the gain medium and photons in a cavity or a chaotic regime
are established. We also find a range of the values of the Fr\"ohlich constant,
the pump rate, and the resonator eigenfrequency, in which more than one
dynamical regime of the system is stable. In this case the laser dynamics is
determined by the initial values of the resonator field, the active medium
polarization, the population inversion, and phonon amplitude.
