Analytical approach for the Floquet theory of delay differential equations

C. Simmendinger, A. Wunderlin, and A. Pelster
Phys. Rev. E 59, 5344 – Published 1 May 1999
PDFExport Citation

Abstract

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.

  • Received 14 October 1998

DOI:https://doi.org/10.1103/PhysRevE.59.5344

©1999 American Physical Society

Authors & Affiliations

C. Simmendinger and A. Wunderlin

  • Institut für Theoretische Physik und Synergetik, Universität Stuttgart, Pfaffenwaldring 57/4, D-70550 Stuttgart, Germany

A. Pelster

  • Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany

References (Subscription Required)

Click to Expand
Issue

Vol. 59, Iss. 5 — May 1999

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×