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.

The Bogdanov map is named after Rifkat Bogdanov.

See also

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References

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  • 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.
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