### 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 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.

Translated title of the contribution | Continuation of bifurcations in periodic delay differential equations using characteristic matrices |
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Original language | English |

Pages (from-to) | 1301 - 1317 |

Number of pages | 17 |

Journal | SIAM Journal on Scientific Computing |

Volume | 28 (4) |

DOIs | |

Publication status | Published - Jul 2006 |

### Bibliographical note

Publisher: Society for Industrial and Applied Mathematics## Fingerprint Dive into the research topics of 'Continuation of bifurcations in periodic delay differential equations using characteristic matrices'. Together they form a unique fingerprint.

## Cite this

Szalai, R., Stépán, G., & Hogan, SJ. (2006). Continuation of bifurcations in periodic delay differential equations using characteristic matrices.

*SIAM Journal on Scientific Computing*,*28 (4)*, 1301 - 1317. https://doi.org/10.1137/040618709