Encyclopedia of Systems Biology

2013 Edition
| Editors: Werner Dubitzky, Olaf Wolkenhauer, Kwang-Hyun Cho, Hiroki Yokota

Dynamical Systems Theory, Bifurcation Analysis

  • Alan ChampneysEmail author
  • Krasimira Tsaneva-Atanasova
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-9863-7_270



Bifurcation theory refers to the study of qualitative changes to the state of a system as a parameter is varied. It can be applied to  steady state systems, or to dynamical systems and can be understood best at the level of a mathematical model, although recent techniques allow the method to be applied to experiments with feedback control. Typically the theory is applied to a  continuous model, but can also be used in  discrete models and mathematics, difference equations. There are dedicated numerical implementations of bifurcation theory using path-following, or numerical continuation. There is a distinction between a local  bifurcation, which can be understood in terms of a change to the number or stability of simple steady states, and a global bifurcation, which cannot. Often global bifurcations cause catastrophic changes to the  attractorof the system. Typical local examples...

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© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  1. 1.Department of Engineering MathematicsUniversity of BristolBristolUK