动力系统实测数据的Lyapunov指数的矩阵算法

The Matric Algorithm of Lyapunov Exponent for the Experimental Date Obtained in Dynamic Analysis

Ｌｙａｐｕｎｏｖ 指数ｌ 是定量描述混沌吸引子的重要指标，自从１９８５ 年 Ｗｏｌｆ 提出 Ｌｙａｐｕｎｏｖ 指数ｌ的轨线算法以来，如何准确、快速地计算正的、最大的 Ｌｙａｐｕｎｏｖ 指数ｌｍａｘ 便成为人们关注的问题，虽有不少成功计算的报导，但一般并不公开交流· 在 Ｚｕｏ Ｂｉｎｇｗｕ 理论算法的基础上，给出了 Ｌｙａｐｕｎｏｖ指数ｌ 的具体的矩阵算法，并与 Ｗｏｌｆ 的算法进行了比较，计算结果表明：算法能快速、准确地计算（ 主要是正的、最大的） Ｌｙａｐｕｎｏｖ 指数ｌｍ ａｘ· 并对 Ｌｙａｐｕｎｏｖ 指数ｌ 的大小所反应的吸引子的特性进行了分析，并得出了相应的结论·

The Lyapunov exponent is important quantitative index for describing chaotic attractors. Since Wolf put up the trajectory algorithm to Lyapunov exponent in 1985, how to calculate the Lyapunov exponent with accuracy has become a very important question. Based on the theoretical algorithm of Zuo Binwu, the matric algorithm of Lyapunov exponent is given, and the results with the results of Wolf's algorithm are compared. The calculating results validate that the matric algorithm has sufficient accuracy, and the relationship between the character of attractor and the value of Lyapunov exponent are studied in this paper. The corresponding conclusions are given in this paper.