Continuation of bifurcations in periodic delay differential equations using characteristic matrices

R Szalai; G Stepan; SJ Hogan

Continuation of bifurcations in periodic delay differential equations using characteristic matrices

R Szalai, G Stepan, SJ Hogan

Research output: Working paper › Working paper and Preprints

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Abstract

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 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.

Original language	English
Publication status	Unpublished - 2004

Bibliographical note

Sponsorship: The authors thank Bernd Krauskopf, Kirk Green and Gabor Orosz for helpful discussion. During the perparation of this work the first author was supported by the Hungarian Eotvos scholarship and the Fulbright Scholarship. The second author
was supported by the Hungarian National Science Foundation under grant no. OTKA T043368.

Keywords

bifurcations
continuation
periodic solutions
delay-differential equations

Access to Document

2004r23Submitted manuscript, 290 KB

http://hdl.handle.net/1983/70

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abstract = "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 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.",

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AU - Stepan, G

AU - Hogan, SJ

N1 - Sponsorship: The authors thank Bernd Krauskopf, Kirk Green and Gabor Orosz for helpful discussion. During the perparation of this work the first author was supported by the Hungarian Eotvos scholarship and the Fulbright Scholarship. The second author was supported by the Hungarian National Science Foundation under grant no. OTKA T043368.

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N2 - 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 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.

AB - 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 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.

KW - bifurcations

KW - continuation

KW - periodic solutions

KW - delay-differential equations

M3 - Working paper and Preprints

BT - Continuation of bifurcations in periodic delay differential equations using characteristic matrices

ER -