article

MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs

Authors:

Yu. A. KuznetsovAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 29, Issue 2

Pages 141 - 164

https://doi.org/10.1145/779359.779362

Published: 01 June 2003 Publication History

Abstract

MATCONT is a graphical MATLAB software package for the interactive numerical study of dynamical systems. It allows one to compute curves of equilibria, limit points, Hopf points, limit cycles, period doubling bifurcation points of limit cycles, and fold bifurcation points of limit cycles. All curves are computed by the same function that implements a prediction-correction continuation algorithm based on the Moore-Penrose matrix pseudo-inverse. The continuation of bifurcation points of equilibria and limit cycles is based on bordering methods and minimally extended systems. Hence no additional unknowns such as singular vectors and eigenvectors are used and no artificial sparsity in the systems is created. The sparsity of the discretized systems for the computation of limit cycles and their bifurcation points is exploited by using the standard Matlab sparse matrix methods. The MATLAB environment makes the standard MATLAB Ordinary Differential Equations (ODE) Suite interactively available and provides computational and visualization tools; it also eliminates the compilation stage and so makes installation straightforward. Compared to other packages such as AUTO and CONTENT, adding a new type of curves is easy in the MATLAB environment. We illustrate this by a detailed description of the limit point curve type.

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Index Terms

MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs
1. Applied computing
  1. Physical sciences and engineering
2. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
  2. Mathematical software

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 29, Issue 2

June 2003

149 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/779359

Issue’s Table of Contents

Copyright © 2003 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 June 2003

Published in TOMS Volume 29, Issue 2

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https://doi.org/10.1016/j.ymssp.2024.111762
Breunung TBalachandran B(2025)Frequency response based identification of nonlinear oscillatorsJournal of Sound and Vibration10.1016/j.jsv.2024.118651594(118651)Online publication date: Jan-2025
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