  With perfectly balanced gain and loss, dynamical systems with indefinite
damping can obey the exact PT-symmetry being marginally stable with a pure
imaginary spectrum. At an exceptional point where the symmetry is spontaneously
broken, the stability is lost via passing through a non-semisimple 1:1
resonance. In the parameter space of a general dissipative system, marginally
stable PT-symmetric ones occupy singularities on the boundary of the asymptotic
stability. To observe how the singular surface governs dissipation-induced
destabilization of the PT-symmetric system when gain and loss are not matched,
an extension of recent experiments with PT-symmetric LRC circuits is proposed.
