Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Numerical Bifurcation Analysis

Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_373-3

Definition of the Subject

The theory of dynamical systems studies the behavior of solutions of systems, like nonlinear ordinary differential equations (ODEs), depending upon parameters. Using qualitative methods of bifurcation theory, the behavior of the system is characterized for various parameter combinations. In particular, the catalog of system behaviors showing qualitative differences can be identified, together with the regions in parameter space where the different behaviors occur. Bifurcations delimit such regions. Symbolic and analytical approaches are in general infeasible, but numerical bifurcation analysis is a powerful tool that aids in the understanding of a nonlinear system. When computing power became widely available, algorithms for this type of analysis matured and the first codes were developed. With the development of suitable algorithms, the advancement in the qualitative theory has found its way into several software projects evolving over time. The availability...

Keywords

Hopf Bifurcation Center Manifold Period Doubling Solution Branch Bifurcation Curve 
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

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Hil G. E. Meijer
    • 1
  • Fabio Dercole
    • 2
  • Bart Oldeman
    • 3
  1. 1.Department of Electrical Engineering, Mathematics and Computer ScienceUniversity of TwenteEnschedeThe Netherlands
  2. 2.Department of Electronics and InformationPolitecnico di MilanoMilanItaly
  3. 3.McGill HPCMcGill UniversityMontrealCanada