Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 28, Issue 4, Pages 1301-1317Publisher
SIAM PUBLICATIONS
DOI: 10.1137/040618709
Keywords
delay-differential equations; periodic solutions; bifurcations; continuation
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In this paper we describe a method for continuing periodic solution bifurcations in periodic delay-differential equations. First, the notion of characteristic matrices of periodic orbits is introduced and equivalence with the monodromy operator is demonstrated. An alternative formulation of the characteristic matrix is given, which can be computed efficiently. Defining systems of bifurcations are constructed in a standard way, including the characteristic matrix and its derivatives. For following bifurcation curves in two parameters, the pseudo-arclength method is used combined with Newton iteration. Two test examples (an interrupted machining model and a traffic model with driver reaction time) conclude the paper. The algorithm has been implemented in the software tool PDDE-CONT.
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