Degenerate Bogdanov-Takens bifurcations in a one-dimensional transport model of a fusion plasma

TitleDegenerate Bogdanov-Takens bifurcations in a one-dimensional transport model of a fusion plasma
Publication TypeJournal Article
Year of Publication2016
AuthorsH.J de Blank, Y.A Kuznetsov, M.J Pekker, D.WM Veldman
JournalPhysica D-Nonlinear Phenomena
Volume331
Pagination13-26
Date PublishedSEP 15
Abstract

Experiments in tokamaks (nuclear fusion reactors) have shown two modes of operation: L-mode and H-mode. Transitions between these two modes have been observed in three types: sharp, smooth and oscillatory. The same modes of operation and transitions between them have been observed in simplified transport models of the fusion plasma in one spatial dimension. We study the dynamics in such a one-dimensional transport model by numerical continuation techniques. To this end the MATLAB package CL\_MATCONTL was extended with the continuation of (codimension-2) Bogdanov-Takens bifurcations in three parameters using subspace reduction techniques. During the continuation of (codimension-2) Bogdanov-Takens bifurcations in 3 parameters, generically degenerate Bogdanov-Takens bifurcations of codimension-3 are detected. However, when these techniques are applied to the transport model, we detect a degenerate Bogdanov-Takens bifurcation of codimension 4. The nearby 1- and 2-parameter slices are in agreement with the presence of this codimension-4 degenerate Bogdanov-Takens bifurcation, and all three types of L-H transitions can be recognized in these slices. The same codimension-4 situation is observed under variation of the additional parameters in the model, and under some modifications of the model. (C) 2016 Elsevier B.V. All rights reserved.

DOI10.1016/j.physd.2016.05.008
Division

FP

Department

IMT

PID

6ef43389fa1b4feb2c9e75d87b672c5b

Alternate TitlePhys. D

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