Counterexamples to a Method for Identifying Hopf Bifurcations Without Eigenvalue Calculation

We give counterexamples to the numerical method for detecting Hopf bifurcations in electric power systems by singularity of a symmetrized Jacobian in Y. Zhou, V. Ajjarapu," A fast algorithm for identification and tracing of voltage and oscillatory stability margin boundaries", IEEE Proceedings, vol.93, no.5, May 2005, p.934-46. The counterexamples include some simple matrix examples and a single machine infinite bus power system