Staircase structure of Shapiro steps

We investigate $IV$-characteristics of coupled Josephson junctions which model the intrinsic Josephson junctions in high temperature superconductors under external electromagnetic radiation. A staircase structure of Shapiro steps is found in the branching region. Its origin is related to the coupling between junctions and their switching from rotating to oscillating states. This conclusion are tested by detailed analysis of the $IV$-characteristics as for total stack and for each junction in the stack. $IV$-curves of junctions in the stack are compared with the average of time derivative of phase difference. Experimental observation of this staircase structure would give us a prove of coupling between junctions and a way for precise measurement of its value. Such investigations would be also useful for a diagnostic of Josephson junctions in the stack.