Discrete Dynamics in Nature and Society
Volume 5 (2000), Issue 3, Pages 203-221

Bifurcation analysis of the Henon map

Erik Mosekilde,2 Zhanybai T. Zhusubaliyev,1 Vadim N. Rudakov,1 and Evgeniy A. Soukhterin2

1Kursk State Technical University, Department of Computer Science, 50 Years of October Street, 94, Kursk 305040, Russia
2Center for Chaos and Turbulence Studies, Department of Physics, Technical University of Denmark, Lyngby 2800, Denmark

Received 15 March 2000

Copyright © 2000 Erik Mosekilde et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Division of the parameter plane for the two-dimensional Hénon mapping into domains of periodic and chaotic oscillations is studied numerically and analytically. Regularities in the occurrence of different motions and transitions are analyzed. It is shown that there are domains in the plane of parameters, where non-uniqueness of motions exists. This may lead to abrupt changes of the character of the dynamics under variation in the parameters, that is, to a sudden transition from one stable cycle to another or to chaotization of the oscillations.