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:

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

The Bogdanov map is named after Rifkat Bogdanov.

See also

• List of chaotic maps

References

• 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