Singularities of the boundaries of stability domains

Abstract

The singularities of the general position which arise on the boundaries of stability domains of a linear, autonomous system of differential equations in a two- or three-dimensional parameter space are investigated. A constructive approach is proposed which enables one to determine the geometry of the singularities (the orientation in space, the magnitude of the angles, etc.) by constructing cones which are tangential to the stability domain using the first derivatives of the matrix operator of the system with respect to the parameters and its eigenvectors and associated vectors at the singular points of the boundary. Examples are presented.