Dynamic properties of asymmetric double Josephson junction stack with quasiparticle imbalance

We study analytically and numerically the influence of the quasiparticle charge imbalance on the dynamics of the asymmetric Josephson stack formed by two inequivalent junctions: the fast capacitive junction $J{J}_1$ and slow non-capacitive junction $J{J}_2$. We find, that the switching of the fast junction into resistive state leads to significant increase of the effective critical current of the slow junction. At the same time, the initial switching of the slow junction may either increase or decrease the effective critical current of the fast junction, depending on ratio of their resistances and the value of the capacitance. Finally, we have found that the slow quasiparticle relaxation (in comparison with Josephson times) leads to appearance of the additional hysteresis on current-voltage characteristics.