常微分方程系统李雅普诺夫特性指数的研究

讨论常微分方程系统李雅普诺夫特性指数的一些基本问题，包括数值计算技术和常微分方程系统任何平衡点以外极限集的李雅普诺夫指数必有一个为零的结论.给出超混沌吸引子必超出3维的结论，指出基于常微分方程求解李雅普诺夫指数的Wolf程序使用中初值的选取对结果的影响.同时提出一种简便可行的计算条件李雅普诺夫指数方法.通过数值研究一些重要模型进一步说明本文的观点及提出的方法.对常微分方程系统任何平衡点以外极限集的李雅普诺夫指数必有一个为零的结论进行了讨论，可以作为分析结果和计算方法的有利工具，在一些工作中被忽视.关键词：

STUDY ON LYAPUNOV CHARACTERISTIC EXPONENTS OF A NONLINEAR DIFFERENTIAL EQUATION SYSTEM

Some basic problems of Lyapunov Characteristic Exponents (LCE) are discussed, including the computational method and the fact that the Lyapunov exponent of any limit set other than an equilibrium point must be zero, namely one of the Lyapunov exponents should vanishes. The conclusion is deduced that the dimension of a hyper-chaotic attractor must be great than 3. The LCEs of several important models are studied, more reasonable results are yielded. An efficient method for calculating the conditional LCEs is suggested. By studying the conditional LCEs of the hyper-chaotic system, we conclude that it cannot be synchronized with only one driving variable. The infection of random initial values in Wolf's program of LCEs computation is pointed out.