Bogdanov map

Short description: Chaotic 2D map related to the Bogdanov–Takens bifurcation

Example with ε=0, k=1.2, μ=0.

In dynamical systems theory, the Bogdanov map is a chaotic 2D map related to the Bogdanov–Takens bifurcation. It is given by the transformation:

[math]\displaystyle{ \begin{cases} x_{n+1} = x_n + y_{n+1}\\ y_{n+1} = y_n + \epsilon y_n + k x_n (x_n - 1) + \mu x_n y_n \end{cases} }[/math]

The Bogdanov map is named after Rifkat Bogdanov.

See also

• List of chaotic maps

References

• DK Arrowsmith, CM Place, An introduction to dynamical systems, Cambridge University Press, 1990.
• Arrowsmith, D. K.; Cartwright, J. H. E.; Lansbury, A. N.; and Place, C. M. "The Bogdanov Map: Bifurcations, Mode Locking, and Chaos in a Dissipative System." Int. J. Bifurcation Chaos 3, 803–842, 1993.
• Bogdanov, R. "Bifurcations of a Limit Cycle for a Family of Vector Fields on the Plane." Selecta Math. Soviet 1, 373–388, 1981.

External links

• Bogdanov map at MathWorld