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Advances in numerical bifurcation software : MatCont

Niels Neirynck (UGent)
(2019)
Author
Promoter
(UGent) , HGE Meijer and (UGent)
Organization
Abstract
The mathematical background of MatCont, a freely available toolbox, is bifurcation theory which is a field of hard analysis. Bifurcation theory treats dynamical systems from a high-level point of view. In the case of continuous dynamical systems this means that it considers nonlinear differential equations without any special form and without restrictions except for differentiability up to a sufficiently high order (in the present state of MatCont never higher than five.) The number of equations is not fixed in advance and neither is the number of variables or the number of parameters, some of which can be active and others not. The aim of bifurcation theory is to understand and classify the qualitative changes of the solutions to the differential equations under variation of the parameters. This knowledge cannot be applied to practical situations without numerical software, except in some artificially constructed situations. Matcont is a toolbox that computes bifurcation diagrams through numerical methods, namely continuation. This dissertation describes the advances and innovations that were made including the detection and continuation of new bifurcations in discrete-time systems.
Keywords
bifurcation software, graphical interface, Matcont, MatcontM, Iterated map, homoclinic orbit

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Citation

Please use this url to cite or link to this publication:

Chicago
Neirynck, Niels. 2019. “Advances in Numerical Bifurcation Software : MatCont”. Ghent, Belgium: Ghent University. Faculty of Sciences.
APA
Neirynck, N. (2019). Advances in numerical bifurcation software : MatCont. Ghent University. Faculty of Sciences, Ghent, Belgium.
Vancouver
1.
Neirynck N. Advances in numerical bifurcation software : MatCont. [Ghent, Belgium]: Ghent University. Faculty of Sciences; 2019.
MLA
Neirynck, Niels. “Advances in Numerical Bifurcation Software : MatCont.” 2019 : n. pag. Print.
@phdthesis{8615817,
  abstract     = {The mathematical background of MatCont, a freely available toolbox, is bifurcation theory which is a field of hard analysis. Bifurcation theory treats dynamical systems from a high-level point of view. In the case of continuous dynamical systems this means that it considers nonlinear differential equations without any special form and without restrictions except for differentiability up to a sufficiently high order (in the present state of MatCont never higher than five.) The number of equations is not fixed in advance and neither is the number of variables or the number of parameters, some of which can be active and others not. The aim of bifurcation theory is to understand and classify the qualitative changes of the solutions to the differential equations under variation of the parameters. This knowledge cannot be applied to practical situations without numerical software, except in some artificially constructed situations. Matcont is a toolbox that computes bifurcation diagrams through numerical methods, namely continuation. This dissertation describes the advances and innovations that were made including the detection and continuation of new bifurcations in discrete-time systems.},
  author       = {Neirynck, Niels},
  language     = {eng},
  pages        = {III, 243},
  publisher    = {Ghent University. Faculty of Sciences},
  school       = {Ghent University},
  title        = {Advances in numerical bifurcation software : MatCont},
  url          = {https://sourceforge.net/projects/matcont/},
  year         = {2019},
}