bifurcationBifurcation2002-04-07 07:20:062008-10-17 14:30:02Definitionbifurcationdynamical systemscatastrophe theory\usepackage{amssymb}
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%\usepackage{xypic}\emph{Bifurcation} refers to the splitting of dynamical systems. The parameter space of a dynamical system is regular if all points in the sufficiently small open neighborhood correspond to the dynamical systems that are equivalent to this one; a parameter point that is not regular is a bifurcation point.
For example, the branching of the Feigenbaum tree is an instance of bifurcation.
A cascade of bifurcations is a precursor to chaotic dynamics.
The topologist Ren\'e Thom in his book on catastrophe theory in biology discusses the cusp bifurcation
as a basic example of (dynamic) `catastrophe' in morphogenesis and biological development.
\begin{thebibliography}{3}
\bibitem{B1} ``Bifurcations'', \PMlinkexternal{http://mcasco.com/bifurcat.html}{http://mcasco.com/bifurcat.html}
\bibitem{B2} ``Bifurcation'', \PMlinkexternal{http://spanky.triumf.ca/www/fractint/bif_type.html}{http://spanky.triumf.ca/www/fractint/bif_type.html}
\bibitem{B3} ``Quadratic Iteration, bifurcation, and chaos'', \PMlinkexternal{http://mathforum.org/advanced/robertd/bifurcation.html}{http://mathforum.org/advanced/robertd/bifurcation.html}
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