Analytical approach for the Floquet theory of delay differential equations

We present an analytical approach to deal with nonlinear delay differential equations close to instabilities of time periodic reference states. To thi s end we start with approximately determining such reference states by exte nding the Poincare-Lindstedt and the Shohat expansions, which were original ly developed for ordinary differential equations. Then we systematically el aborate a linear stability analysis around a time periodic reference state. This allows us to approximately calculate the Floquet eigenvalues and thei r corresponding eigensolutions by using matrix valued continued fractions. [S1063-651X(99)14005-4].