Bogdanov map

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

Example with ε=0, k=1.2, μ=0.

${\begin{cases}x_{n+1}=x_{n}+y_{n+1}\\y_{n+1}=y_{n}+\epsilon y_{n}+kx_{n}(x_{n}-1)+\mu x_{n}y_{n}\end{cases}}$

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