On the Floquet Theory of Delay Differential Equations

Details On the Floquet Theory of Delay Differential Equations On the Floquet Theory of Delay Differential Equations

2001-06-16

arxiv.org/abs/math-ph/0106011v1

Physical Review E 59, 5344-5353 (1999)

Physics

Mathematical Physics

Scientific paper

10.1103/PhysRevE.59.5344

We present an analytical approach to deal with nonlinear delay differential equations close to instabilities of time periodic reference states. To this end we start with approximately determining such reference states by extending the Poincar'e Lindstedt and the Shohat expansions which were originally developed for ordinary differential equations. Then we systematically elaborate a linear stability analysis around a time periodic reference state. This allows to approximately calculate the Floquet eigenvalues and their corresponding eigensolutions by using matrix valued continued fractions.

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