Some basic remarks on eigenmode expansions of time-delay dynamics

✍ Scribed by Andreas Amann; Eckehard Schöll; Wolfram Just

• Book ID: 104078133
• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 346 KB
• Volume: 373
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2005.12.073

✦ Synopsis

We describe in elementary terms how eigenmode expansions can be used to deal with differential-difference equations.

As particular applications we present the full analytical solution of linear stochastic time-delay systems and the weakly nonlinear analysis of nonlinear differential-difference equations in the limit of large time delay. Our exposition is essentially based on an explicit analytical expression for the linear spectrum in terms of the Lambert W-function and on the explicit formula for the eigenfunctions of the adjoint equation.