  Theoretical study is performed of a single-mode polariton system with linear
coupling of spin components. When combined with an ordinary two-particle
interaction, the spin coupling involves a spontaneous symmetry breaking
accompanied by a switch from linear to circular polarization under resonant
driving. The asymmetric steady states can also lose stability, giving way to
oscillatory and chaotic dynamics. Here, we explore a continuous transformation
between the multistable regime, where the system is steady and locked in phase
to the pump but has a broken spin symmetry, and full-span oscillations of the
circular-polarization degree, owing to which the symmetry is effectively
reestablished. Such oscillations are analogous to the intrinsic Josephson
effect and prove to be robust against arbitrarily strong perturbations.
Transitional phenomena include the Hopf bifurcation, spin bistability of limit
cycles, and continuous transitions to and from dynamical chaos through series
of period doubling/halving events.
