PT-symmetry, indefinite damping and dissipation-induced instabilities

► A direct link is established between the PT-symmetry and dissipation-induced instabilities. ► Exactly PT-symmetric systems are singularities on the asymptotic stability threshold of the indefinitely damped ones. ► Destabilizing influence of dissipation can be tested in experiments with LRC circuits. ► A singular threshold of the modulational instability is established that explains its enhancement with dissipation.