Bogachev V.M.

The main properties of the characteristic equation root trajectories for the complex coefficients and for the complex absolute parameter are considered. These equations occur at stability studying of selective systems by the symbolic abbreviated equation method as well as for other cases. The relations between the root trajectories with the phase paths of associated dynamic system of second order that opens the new possibilities for investigation the general topology properties of the locus with the complex (in particular, real) parameter are considered.