We show that the Coulomb blockade in parallel dots pierced by magnetic flux $Phi$ completely blocks the resonant current for any value of $Phi$ except for integer multiples of the flux quantum $Phi_0$. This non-analytic (switching) dependence of the
current on $Phi$ arises only when the dot states that carry the current are of the same energy. The time needed to reach the steady state, however, diverges when $Phito nPhi_0$.
We study the relationship between the partial synchronous (PaS) state and the coupling structure in general dynamical systems. By the exact proof, we find the sufficient and necessary condition of the existence of PaS state for the coupling structure
. Our result shows that the symmetry of the coupling structure is not the equivalent condition which is supposed before but only the sufficient condition. Furthermore, for the existence of the PaS state, the general structure is the equal-degree random.
