Some basic remarks on eigenmode expansions of time-delay dynamics

Andreas Amann, Eckehard Schöll and Wolfram Just

Physica A: Statistical Mechanics and its Applications, 2007, vol. 373, issue C, 191-202

Abstract: 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.

Keywords: Functional differential equation; Stochastic systems; Centre manifold reduction (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:373:y:2007:i:c:p:191-202

DOI: 10.1016/j.physa.2005.12.073

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