BifurcationMathworldPlanetmath refers to the splitting of dynamical systemsMathworldPlanetmathPlanetmath. 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 equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath 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.


  • 1 “Bifurcations”,
  • 2 “Bifurcation”,
  • 3 “Quadratic Iteration, bifurcation, and chaos”,
Title bifurcation
Canonical name Bifurcation
Date of creation 2013-03-22 12:34:21
Last modified on 2013-03-22 12:34:21
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 11
Author CWoo (3771)
Entry type Definition
Classification msc 34C23
Classification msc 35B32
Classification msc 37H20
Related topic DynamicalSystem
Related topic SystemDefinitions