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 René 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.

Bibliography

1

``Bifurcations'', http://mcasco.com/bifurcat.html

2

``Bifurcation'', http://spanky.triumf.ca/www/fractint/bif_type.html

3

``Quadratic Iteration, bifurcation, and chaos'', http://mathforum.org/advanced/robertd/bifurcation.html