Phys. Rev. E 59, 5344–5353 (1999)Analytical approach for the Floquet theory of delay differential equationsReceived 14 October 1998; published in the issue dated May 1999 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 Poincaré-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 us to approximately calculate the Floquet eigenvalues and their corresponding eigensolutions by using matrix valued continued fractions. © 1999 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.59.5344
DOI:
10.1103/PhysRevE.59.5344
PACS:
05.45.-a, 02.30.Ks
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