Title: Bifurcation analysis of periodic solutions of neutral functional differential equations: A case study
Authors: Engelborghs, Koen ×
Roose, Dirk
Luzyanina, T #
Issue Date: Oct-1998
Publisher: World scientific publ co pte ltd
Series Title: International journal of bifurcation and chaos vol:8 issue:10 pages:1889-1905
Abstract: This paper deals with the numerical bifurcation analysis of periodic solutions of a system of neutral functional differential equations (NFDEs). Compared with retarded functional differential equations, the solution operator of a system of NFDEs does not smooth the initial data as time increases and it is no longer a compact operator. The stability of a periodic solution is determined both by the point spectrum and by the essential spectrum of the Poincare operator. We show that a periodic solution can change its stability not only by means of a "normal" bifurcation but also when the essential spectrum crosses the unit circle. In order to monitor the essential spectrum during continuation, we derive an upper bound on its spectral radius. The upper bound remains valid even at paints where the radius of the essential spectrum is noncontinuous. This can occur when the delay and the period are rationally dependent. Our numerical results present these new dynamical phenomena and we state a number of open questions. Although we restrict our discussion to a specific example, we strongly believe that the issues we discuss are representative for a general class of NFDEs.
ISSN: 0218-1274
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

Files in This Item:

There are no files associated with this item.

Request a copy


All items in Lirias are protected by copyright, with all rights reserved.

© Web of science