  We present a model for theoretical description of the dynamics of a system of
spinor cavity polaritons in real space and time accounting for all relevant
types of the interactions and effective magnetic fields. We apply our general
formalism for the consideration of the polarization dynamics of the coherently
driven one dimensional polariton channel. We investigate effect of the
temperature and the longitudinal-transverse splitting on the spin
(polarization) multistability and hysteresis arising from the
polarization-dependent polariton-polariton interaction. We show that the effect
of the phase of the driving laser pump is as important as its strength and
demonstrate that the multistability behavior can survive up to high
temperatures in presence of longitudinal-transverse splitting.
