Bogdanov Map

A 2-D Map which is conjugate to the Hénon Map in its nondissipative limit. It is given by

$$x' = x+y'$$

$$y' = y+\epsilon y+kx(x-1)+\mu xy.$$

See also Hénon Map

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.