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 |