New features of the software M at C ont for bifurcation analysis of dynamical systems

A. Dhooge, W. Govaerts, Yu. A. Kuznetsov, H. G.E. Meijer and B. Sautois

Mathematical and Computer Modelling of Dynamical Systems, 2007, vol. 14, issue 2, 147-175

Abstract: Bifurcation software is an essential tool in the study of dynamical systems. From the beginning (the first packages were written in the 1970's) it was also used in the modelling process, in particular to determine the values of critical parameters. More recently, it is used in a systematic way in the design of dynamical models and to determine which parameters are relevant. M at C ont and C l _M at C ont are freely available matlab numerical continuation packages for the interactive study of dynamical systems and bifurcations. M at C ont is the GUI-version, C l _M at C ont is the command-line version. The work started in 2000 and the first publications appeared in 2003. Since that time many new functionalities were added. Some of these are fairly simple but were never before implemented in continuation codes, e.g. Poincaré maps. Others were only available as toolboxes that can be used by experts, e.g. continuation of homoclinic orbits. Several others were never implemented at all, such as periodic normal forms for codimension 1 bifurcations of limit cycles, normal forms for codimension 2 bifurcations of equilibria, detection of codimension 2 bifurcations of limit cycles, automatic computation of phase response curves and their derivatives, continuation of branch points of equilibria and limit cycles. New numerical algorithms for these computations have been published or will appear elsewhere; here we restrict to their software implementation. We further discuss software issues that are in practice important for many users, e.g. how to define a new system starting from an existing one, how to import and export data, system descriptions, and computed results.

Date: 2007
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DOI: 10.1080/13873950701742754

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