On roots and charts of delay equations with complex coefficients

This work is devoted to the analytic study of the characteristic roots of scalar autonomous Delay Differential Equations (DDEs) with complex coefficients. The focus is placed on the robust analysis of the position of the roots in C with respect to the variation of the coefficients, with the final aim of obtaining suitable representations for the relevant stability boundaries and charts. The investigation benefits from a preliminary shift of the coefficients which reduces the number of free parameters allowing for useful graphical visualizations. The present research is motivated on the base of studying the stability of systems of DDEs.