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DSWeb Dynamical Systems Software aims to collect all available software on dynamical systems theory. This project was originally launched during the special year Emerging Applications of Dynamical Systems, 1997/1998, at the Institute for Mathematics and its Applications. The information here includes functionality, platforms, languages, references, and contacts.

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MatCont

By Annick Dhooge
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MatCont and CL_MatCont: continuation software in Matlab

The study of differential equations requires good and powerful mathematical software. Also, a flexible and extendible package is important. A powerful and widely used environment for scientific computing is MATLAB. The aim ofMatCont and Cl_MatCont is to provide a continuation toolbox which is compatible with the standard MATLAB ODE representation of differential equations.

MatCont is a graphical MATLAB package for the interactive numerical study of a range of parameterized nonlinear problems. The current version is freely available at http://www.matcont.UGent.be where also a slightly more general non–GUI version Cl_MatCont is available.

 

The following functions are supported by the present version of MatCont :

  • continuation of equilibrium and periodic solutions with respect to a control parameter;
  • detection of fold, Hopf and branching points on curves of equilibria;
  • normal form analysis of fold and Hopf equilibrium bifurcations;
  • continuation of fold and Hopf equilibrium bifurcations in two control parameters;
  • detection of all codim 2 equilibrium bifurcations (cusp, Bogdanov-Takens, generalized Hopf, zero-Hopf, and double Hopf) on fold and Hopf curves;
  • detection of branch bifurcation points on fold curves;
  • continuation of branch points of equilibria in three control parameters;
  • detection of flip, fold, torus and branch bifurcations of periodic solutions;
  • continuation of flip, fold and torus bifurcations of periodic solutions in two control parameters;
  • continuation of the period doubled branch in a flip point;
  • continuation of branch bifurcations of periodic solutions in three control parameters;
  • makes the MATLAB odesuite for time integration interactively available;
  • can use the MATLAB Symbolic Toolbox for computing derivatives whenever it is installed.
  • the archive filter limits the number of curves of a particular type;
  • branch switching at branch points of equilibria and limit cycles;
  • user functions can be added;
  • computation of normal form coefficients for bifurcations of periodic solutions;
  • detection of several codim 2 bifurcations on fold, flip and torus bifurcation curves;
  • help function.
KeywordsBifurcation analysis, Continuation, Dynamics (phase diagrams), Visualization
Model
  • ODEs
Software Type
  • Package
Language
  • MatLab
Platform
  • Unix
  • Linux
  • Windows
  • MacOS
Availability
The package is freely available for scientific use: http://www.matcont.UGent.be
Contact Person
Annick Dhooge, Ghent University, [email protected]
References to Papers
  • (A. Dhooge, W. Govaerts, Yu. A. Kuznetsov, W. Mestrom and A.M. Riet) Cl_matcont : A continuation toolbox in Matlab, Proceedings of the 2003 ACM Symposium on Applied Computing (Melbourne, Florida, USA, March 2003) ISBN 1-58113-624-2, pp. 161 - 166.
  • (A. Dhooge, W. Govaerts and Yuri A. Kuznetsov) Numerical Continuation of Fold bifurcations of Limit Cycles in MATCONT, Proceedings of the International Conference on Computational Science ICCS 2003,Melbourne, Australia and St Petersburg, Russia, 2-4 June 2003, Part I. Springer Verlag Lecture Notes in Computer Science, Vol. 2657 (May 2003) (eds. P.M.A. Sloot, D. Abramson, A.V. Bogdanov, J.J. Dongarra, A.Y. Zomaya and Y.E. Gorbachev). ISBN 3-540-40194-6, pp. 701-710.
  • (A. Dhooge, W. Govaerts and Yuri A. Kuznetsov) Bifurcations of Periodic Solutions of ODEs using Bordered Systems, NaCom Extended Abstracts, pp. 61-64. Proceedings of the International Conference on Numerical Analysis and Computational Mathematics, Anglia Polytechnic University, 23-26 May 2003, Cambridge, UK (ed. G. Psihoyios), ISBN 3-527-40462-7. J. Wiley (2003).
  • (A. Dhooge, W. Govaerts and Yuri A. Kuznetsov)MatCont: A Matlab package for numerical bifurcation analysis of ODEs, ACM Transactions on Mathematical Software 29(2) (2003), pp. 141-164.
  • (A. Dhooge, W. Govaerts and Yu.A. Kuznetsov), MatCont: a Matlab package for numerical bifurcation analysis of ODEs, ACM Sigsam Bulletin, Volume 38, Issue 1, March 2004, pp. 21-22. (Abstract of the ISSACS 2003 software exhibition, Philadelphia, 2003).
  • (A. Dhooge, W. Govaerts and Yuri A. Kuznetsov), Numerical continuation of branch points of limit cycles in MatCont, Proceedings of the International Conference on Computational Science ICCS 2004, Krakow, Poland, 6-9 June 2004, Part II. Springer Verlag Lecture Notes in Computer Science Vol. 3037, 2004 (eds. Bubak, M.; Albada, G.D.v.; Sloot, P.M.A.; Dongarra, J.J.), pp. 42-49. ISBN: 3-540-22115-8
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