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Interactive initialization and continuation of homoclinic and heteroclinic orbis in MATLAB

Virginie De Witte UGent, Willy Govaerts UGent, Yuri Kuznetsov and Mark Friedman (2012) ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE. 38(3).
abstract
MATCONT is a MATLAB continuation package for the interactive numerical study of a range of parameterized nonlinear dynamical systems, in particular ODEs, that allows to compute curves of equilibria, limit points, Hopf points, limit cycles, flip, fold and torus bifurcation points of limit cycles. It is now possible to continue homoclinic-to-hyperbolic-saddle and homoclinic-to-saddle-node orbits in MATCONT. The implementation is done using the continuation of invariant subspaces, with the Riccati equations included in the defining system. A key feature is the possibility to initiate both types of homoclinic orbits interactively, starting from an equilibrium point and using a homotopy method. All known codimension-two homoclinic bifurcations are tested for during continuation. The test functions for inclination-flip bifurcations are implemented in a new and more efficient way. Heteroclinic orbits can now also be continued and an analogous homotopy method can be used for the initialization.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Global bifurcation, homotopy, numerical continuation, LOCATING CONNECTING ORBITS, INVARIANT SUBSPACES, NUMERICAL COMPUTATION, BIFURCATION-ANALYSIS
journal title
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
ACM Trans. Math. Softw.
volume
38
issue
3
article_number
18
pages
34 pages
Web of Science type
Article
Web of Science id
000303654900003
JCR category
MATHEMATICS, APPLIED
JCR impact factor
1.934 (2012)
JCR rank
13/247 (2012)
JCR quartile
1 (2012)
ISSN
0098-3500
DOI
10.1145/2168773.2168776
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
2129354
handle
http://hdl.handle.net/1854/LU-2129354
date created
2012-06-01 15:30:25
date last changed
2012-06-18 13:36:07
@article{2129354,
  abstract     = {MATCONT is a MATLAB continuation package for the interactive numerical study of a range of parameterized nonlinear dynamical systems, in particular ODEs, that allows to compute curves of equilibria, limit points, Hopf points, limit cycles, flip, fold and torus bifurcation points of limit cycles. It is now possible to continue homoclinic-to-hyperbolic-saddle and homoclinic-to-saddle-node orbits in MATCONT. The implementation is done using the continuation of invariant subspaces, with the Riccati equations included in the defining system. A key feature is the possibility to initiate both types of homoclinic orbits interactively, starting from an equilibrium point and using a homotopy method. All known codimension-two homoclinic bifurcations are tested for during continuation. The test functions for inclination-flip bifurcations are implemented in a new and more efficient way. Heteroclinic orbits can now also be continued and an analogous homotopy method can be used for the initialization.},
  articleno    = {18},
  author       = {De Witte, Virginie and Govaerts, Willy and Kuznetsov, Yuri and Friedman, Mark},
  issn         = {0098-3500},
  journal      = {ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE},
  keyword      = {Global bifurcation,homotopy,numerical continuation,LOCATING CONNECTING ORBITS,INVARIANT SUBSPACES,NUMERICAL COMPUTATION,BIFURCATION-ANALYSIS},
  language     = {eng},
  number       = {3},
  pages        = {34},
  title        = {Interactive initialization and continuation of homoclinic and heteroclinic orbis in MATLAB},
  url          = {http://dx.doi.org/10.1145/2168773.2168776},
  volume       = {38},
  year         = {2012},
}

Chicago
De Witte, Virginie, Willy Govaerts, Yuri Kuznetsov, and Mark Friedman. 2012. “Interactive Initialization and Continuation of Homoclinic and Heteroclinic Orbis in MATLAB.” Acm Transactions on Mathematical Software 38 (3).
APA
De Witte, Virginie, Govaerts, W., Kuznetsov, Y., & Friedman, M. (2012). Interactive initialization and continuation of homoclinic and heteroclinic orbis in MATLAB. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 38(3).
Vancouver
1.
De Witte V, Govaerts W, Kuznetsov Y, Friedman M. Interactive initialization and continuation of homoclinic and heteroclinic orbis in MATLAB. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE. 2012;38(3).
MLA
De Witte, Virginie, Willy Govaerts, Yuri Kuznetsov, et al. “Interactive Initialization and Continuation of Homoclinic and Heteroclinic Orbis in MATLAB.” ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 38.3 (2012): n. pag. Print.