Pseudospectral methods for stability analysis of delayed dynamical systems

In order to investigate the local stability of both equilibria and periodic orbits of delayed dynamical systems we employ the numerical method recently proposed by the authors for discretizing the associated evolution family. The objective is the efficient computation of stability charts for varying or uncertain system parameters. A benchmark set of tests is provided including computational data such as the accuracy of the stability boundaries and the total computational time, with particular reference to the delayed Mathieu equation. © 2013, Springer-Verlag Berlin Heidelberg.