Abstract
matcont is a matlab continuation package for the interactive numerical study of a range of parameterized nonlinear problems. We discuss a recent addition to the package, namely the continuation of branch points of limit cycles in three parameters which is not available in any other package. This includes the exact location of the BPC points and branch switching. The algorithm is important in the numerical study of symmetry and we illustrate it in the case of the famous Lorenz model for the atmospheric circulation.
Chapter PDF
Similar content being viewed by others
References
Beyn, W.J., Champneys, A.R., Doedel, E., Govaerts, W.: Numerical continuation and computation of normal forms. In: Fiedler, B. (ed.) Handbook of Dynamical Systems, vol. 2, pp. 149–219. Elsevier, Amsterdam (2002)
Dhooge, A., Govaerts, W., Kuznetsov, Y.A.: matcont: A matlab package for numerical bifurcation analysis of ODEs. ACM TOMS 29(2), 141–164 (2003)
Dhooge, A., Govaerts, W., Kuznetsov, Y.A., Mestrom, W., Riet, A.M. : A Continuation Toolbox in matlab (2003) (manual) , http://allserv.UGent.be/~ajdhooge/doc_cl_matcont.zip
Dhooge, A., Govaerts, W., Kuznetsov, Y.A.: Numerical continuation of fold bifurcations of limit cycles in matcont. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Gorbachev, Y.E., Dongarra, J., Zomaya, A.Y. (eds.) ICCS 2003. LNCS, vol. 2657, pp. 701–710. Springer, Heidelberg (2003)
Doedel, E.J., Champneys, A.R., Fairgrieve, T.F., Kuznetsov, Y.A., Sandstede, B., Wang, X.J.: auto97-auto2000 : Continuation and Bifurcation Software for Ordinary Differential Equations (with HomCont), User’s Guide, Concordia University, Montreal, Canada (1997–2000), http://indy.cs.concordia.ca
Doedel, E.J., Govaerts, W., Kuznetsov, Y.A.: Computation of periodic solution bifurcations in ODEs using bordered systems. SIAM J. Numer. Anal. 41(2), 401–435 (2003)
Doedel, E.J., Govaerts, W., Kuznetsov, Y.A., Dhooge, A.: Numerical continuation of branch points of equilibria and periodic orbits, Preprint 1280, Department of Mathematics, Utrecht University, The Netherlands (2003)
Govaerts, W.: Numerical Methods for Bifurcations of Dynamical Equilibria. SIAM, Philadelphia (2000)
Kuznetsov, Y.A.: Elements of Applied Bifurcation Theory, 2nd edn. Springer, New York (1998)
Kuznetsov, Y.A., Levitin, V.V.: content: Integrated Environment for Analysis of Dynamical Systems. CWI, Amsterdam (1997), ftp://ftp.cwi.nl/pub/CONTENT
Lorenz, E.: Deterministic non-periodic flow. J. Atmos. Science 20, 130–141 (1963)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dhooge, A., Govaerts, W., Kuznetsov, Y.A. (2004). Numerical Continuation of Branch Points of Limit Cycles in MATCONT. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science - ICCS 2004. ICCS 2004. Lecture Notes in Computer Science, vol 3037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24687-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-24687-9_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22115-9
Online ISBN: 978-3-540-24687-9
eBook Packages: Springer Book Archive