Kawakami映射的超混沌行为研究  

STUDY ON STRANGE HYPER-CHAOTIC DYNAMICS OF KAWAKAMI MAP

作　　者：何岱海[1] 徐健学[1] 陈永红[1] 

机构地区：[1]西安交通大学非线性动力学研究所,西安710049

出　　处：《力学学报》2000年第6期750-754,共5页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(19972051)

摘　　要：通过对一类平面二维映射系统非线性动力学行为的分析，发现该系统存在一个奇怪吸引子，该吸引子具有两个正Ｌｙａｐｕｎｏｖ指数和分数维．通过该系统不动点的分析揭示了该吸引子的吸引域边界结构，即不稳定第二类结点与不稳定偶数周期点在吸引域边界上的相间排列．The strange hyper-chaotic dynamics of several noninvertible two-dimensional map systems with two positive Lyapunov exponents are studied in this paper. These systems have spreading attractors. As an example the Kawakami map is studied more thorough. The characters of the fixed points, chaotic attractor and attractive basin are analyzed. The phenomena that the second unstable node is on the attractive basin boundary and the structure that the even unstable periodic points are arranged on the boundary is found and analyzed. The second unstable node and the unstable even periodic points and their stable flow are arranged on the boundary of the attractive basin. This structure especially with the second node is reported and studied rarely. The dynamics of n dimensional map yielding n positive Lyapunov exponents is only detailedly studied for the case of n =1 before. The results in this paper show that such a situation can be met for n = 2. The attractors spread in a zone with complicate structure. This is different from the common strange attractors contract to a low dimensional manifold like Henon map. Because the attractor of Kawakami map also has a non-integer dimension, the geometry structure in state plane should be strange. A conclusion can be drawn, if a two-dimensional map has only two unstable fixed point, a node and a focus, and there is a attractive set surrounding the focus, the attractive set must have a bounded attractive basin and the unstable node on the boundary. If the node is unstable second node, there must be even periodic point on the boundary.

关 键 词：非线性动力学 不可逆映射 奇怪吸引子 KAwAkAmi映射 超混沌行为 

分 类 号：O322[理学—一般力学与力学基础] O415.5[理学—力学]