Discrete Dynamics in Nature and Society
Volume 5 (2000), Issue 3, Pages 203-221
doi:10.1155/S1026022600000534
Bifurcation analysis of the Hénon map
Zhanybai T. Zhusubaliyev1
, Vadim N. Rudakov2
, Evgeniy A. Soukhoterin2
and Erik Mosekilde1
1Center for Chaos and Turbulence Studies, Department of Physics, Technical University of Denmark, Lyngby 2800, Denmark
2Kursk State Technical University, Department of Computer Science, 50 Years of October Street, 94, Kursk 305040, Russia
Abstract
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.