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In dynamical systems theory, the Bogdanov map is a
Bogdanov map
at MathWorld Chaotic maps Exactly solvable models Dynamical systems {{fractal-stub
In dynamical systems theory, the Bogdanov map is a chaotic
Chaotic was originally a Danish trading card game. It expanded to an online game in America which then became a television program based on the game. The program was able to be seen on 4Kids TV (Fox affiliates, nationwide), Jetix, The CW4Kid ...
2D map related to the Bogdanov–Takens bifurcation. It is given by the transformation:
:
The Bogdanov map is named after Rifkat Bogdanov Rifkat Ibragimovich Bogdanov (russian: Рифка́т Ибраги́мович Богда́нов; June 13, 1950 – November 3, 2013) was a Soviet and Russian mathematician known for contributions to nonlinear dynamical systems, bifurcation th ...
.
See also
*List of chaotic maps
In mathematics, a chaotic map is a map (namely, an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functi ...
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 Chaotic maps Exactly solvable models Dynamical systems {{fractal-stub