The dynamics of exciton-polariton states in a semiconductor microresonator has been studied when pumping the state corresponding to the lower polariton branch considering single-mode and intermode elastic polariton-polariton interactions. In this case, the pumping has been carried out by two laser pulses with close frequencies. It has been shown that at the initial phase difference equal to , the mode of quantum self-capture of exciton-polaritons is observed. The periodic and aperiodic modes of evolution of a system of quasiparticles have been obtained.