The Josephson plasma mode (JPM) in layered cuprate superconductors is strongly affected by the external tunneling injection and/or by the ac field applied. In the model of the c axis tunneling transport, the dielectric function &egr;(&ohgr;) is calculated. For the cases of the tunneling injection and of the microwave, we obtain the conditions when the JPR is shifted and vanishes. It causes the arising of a non-equilibrium instability in respect to the transition into a ferroelectric state characterized by a genuine bias voltage along the c axis of a cuprate superconductor sample that can be observed experimentally. ©1999 American Institute of Physics.