The numerical integration of the non-stationary two-dimensional Schrödinger equation is carried out. The dynamical properties (dynamical averages, frequency spectra, uncertainty relations, autocorrelators) for two quantum oscillators coupled by the Pallen- Edmonds potential are studied. As a result of the numerical simulations, it was established that the quantum system is sensitive to small changes in Hamiltonian that are caused by the Pallen-Edmonds coupling potential. In the regime of weak coupling high-frequency oscillations are generated, the spectral component number is increased at amplification of coupling.