Interactive initialization and continuation of homoclinic and heteroclinic orbis in MATLAB
(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:
http://hdl.handle.net/1854/LU-2129354
- author
- Virginie De Witte UGent, Willy Govaerts UGent, Yuri Kuznetsov and Mark Friedman
- organization
- year
- 2012
- 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.