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# 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.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

Keywords:

bifurcation, dynamical systems, catastrophe theory

Related:

DynamicalSystem,SystemDefinitions

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

34C23*no label found*35B32

*no label found*37H20

*no label found*

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