An analytical solution has been found to describe dynamic processes in a superconducting nanointerferometer with negligibly low inductances that is included in a high-Q factor resonator. The effect of nonlinearity in the system, as well as the effect of external parametric pumping, has been analyzed. The screening of detected dynamic modes in the studied nanostructure in the resonator is performed in a wide range and their positions on the plane of the parameters have been determined. A significant influence of phase effects on the evolution of the system has been demonstrated and phase relations allowing one to control the output signal intensity have been evaluated. The detected effects open new possibilities for developing and testing basic elements of modern quantum computing systems.