Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL

By Koen Engelborghs, Tatyana Luzyanina, Dirk Roose. TOMS, 2002

784 citations recorded by the source corpus.

Subfields: Cognitive Neuroscience, Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/16af68d69d9c9223cd2cff5590becc7ea8ce3a01

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In Cognitive Neuroscience

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Citations in the corpus

Galerkin projections for state-dependent delay differential equations with applications to drilling (2013, methodology): “Numerical techniques for treatment of DDEs are still evolving, see for example [9–14].”
Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers (2013, methodology): “Particularly, continuation methods were made accessible for delay systems (Engelborghs, Luzyanina, and Roose, 2002) and allowed for an insightful analysis of the delayed-feedback laser and to identify how different bifurcations connect.”
Continuation and Bifurcation Analysis of Delay Differential Equations (2007, methodology): “By contrast, the software packages DDE-Biftool and PDDE-Contimplement numerical continuation DDEs as introduced in the previous sections.”
Small-Signal Stability Analysis of Large Power Systems With Inclusion of Multiple Delays (2016, methodology): “Further details on this technique can be found in the DDE-BIFTOOL documentation and source code [30].”
Bifurcations and multiple traffic jams in a car-following model with reaction-time delay (2005, methodology): “Preprint submitted to Elsevier Science 20 December 2004”
Criticality of Hopf bifurcation in state-dependent delay model of turning processes (2008, methodology): “The diagrams were determined using the software package DDE-BIFTOOL (see, [34,35]).”
QPmR - Quasi-Polynomial Root-Finder: Algorithm Update and Examples (2014, methodology): “The well known software tool DDE-BIFTOOL [10], see also [20], is the key result of this direction.”