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Interactive Continuation Tools

  • Willy Govaerts
  • Yuri A Kuznetsov

Systematic bifurcation analysis requires the repeated continuation of different phase objects in free parameters, the detection and analysis of their bifurcations, and branch switching. Such computations produce a lot of numerical data that must be analyzed and, finally, presented in graphical form. Thus, continuation programs should not only be effecient numerically but should allow for interactive management and have a user-friendly graphics interface. The development of such programs is progressing rapidly. Here we make an attempt to survey existing interactive continuation and bifurcation tools and outline their history and perspectives. This is followed by the presentation of a framework that organizes the different types of objects and bifurcating branches.We give a brief over view of how such a frame work is implemented in the recent software environment MATCONT. In the final two sections we give a few examples that illustrate the use of MATCONT and indicate directions of future developments.

Keywords

Hopf Bifurcation Bifurcation Point Invariant Manifold Unstable Manifold Homoclinic Orbit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Canopus Publishing Limited 2007

Authors and Affiliations

  • Willy Govaerts
    • 1
  • Yuri A Kuznetsov
    • 2
  1. 1.Department of Applied Mathematics and Computer ScienceGhent UniversityBelgium
  2. 2.Department of MathematicsUtrecht UniversityNetherlands

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