  The topological property of a system is a static property in general. For
instance, the topological edge state is observed by measuring the local density
of states. In this work we propose a system whose topological property is only
revealed by dynamics. As a concrete example, we explore a nonlinear dynamical
topological phase transition revealed by a quench dynamics of a Cooper-pair box
array connected with capacitors. It is described by coupled nonlinear
differential equations due to the Josephson effect. It is trivial as far as the
static system is concerned. However, the wave propagation induced by the quench
dynamics demonstrates a rich topological phase diagram in terms of the strength
of the input.
