Continuation of Bifurcations in Periodic Delay-Differential Equations Using Characteristic Matrices

Abstract. In this paper we describe a method for continuing periodic solution bifurcations in periodic delaydifferential equations. First, the notion of characteristic matrices of periodic orbits is introduced and equivalence with the monodromy operator is proved. An alternative formulation of the characteristic matrix is given, which can efficiently be computed. 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. As a test example, an interrupted machining model is analyzed.