In dynamical systems theory, the Bogdanov map is a chaotic 2D map related to the Bogdanov–Takens bifurcation. It is given by the transformation:
{ x n + 1 = x n + y n + 1 y n + 1 = y n + ϵ y n + k x n ( x n − 1 ) + μ x n y n {\displaystyle {\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