research-article

Interactive Initialization and Continuation of Homoclinic and Heteroclinic Orbits in MATLAB

Authors:

Virginie De Witte,

Willy Govaerts,

Yuri A. Kuznetsov,

Mark FriedmanAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 38, Issue 3

Article No.: 18, Pages 1 - 34

https://doi.org/10.1145/2168773.2168776

Published: 01 April 2012 Publication History

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.

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Interactive Initialization and Continuation of Homoclinic and Heteroclinic Orbits in MATLAB

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 38, Issue 3

April 2012

157 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/2168773

Issue’s Table of Contents

Copyright © 2012 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 01 April 2012

Accepted: 01 September 2011

Revised: 01 September 2011

Received: 01 June 2010

Published in TOMS Volume 38, Issue 3

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Karatetskaia EKoryakin VSoldatkin KKazakov A(2024)Routes to Chaos in a Three-Dimensional Cancer ModelRegular and Chaotic Dynamics10.1134/S156035472405001029:5(777-793)Online publication date: 2-Oct-2024
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