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

## References

- 1 “Bifurcations”, http://mcasco.com/bifurcat.htmlhttp://mcasco.com/bifurcat.html
- 2 “Bifurcation”, http://spanky.triumf.ca/www/fractint/bif_type.htmlhttp://spanky.triumf.ca/www/fractint/bif_type.html
- 3 “Quadratic Iteration, bifurcation, and chaos”, http://mathforum.org/advanced/robertd/bifurcation.htmlhttp://mathforum.org/advanced/robertd/bifurcation.html

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 |