bifurcation

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 bifurcationas a basic example of (dynamic) ‘catastrophe’ in morphogenesis and biological development.