信息熵和HQ准则在最大Lyapunov指数计算中的应用

Application of information entropy and HQ rule in estimating largest Lyapunov exponent

最大Lyapunov指数是判断时间序列是否为混沌的一个重要判据,目前应用比较广泛的是小数据量法。将信息熵和HQ准则应用在最大Lyapunov指数的算法中,改进了小数据量法。信息熵优化了相空间重构参数,克服了独立求解重构参数的不足;利用HQ准则确定邻近点个数增加了计算时的精度。仿真实验表明该改进的小数据量法在计算最大Lyapunov时具有良好的准确性,对噪声具有良好的鲁棒性。

The largest Lyapunov exponent is an essential criterion to judge if a time series is chaos or not. The small-data method is widely used in chaotic characteristic extraction at present. Here,the information entropy and HQ rule were applied in estimating the largest Lyapunov exponent to improve the small-data method. The information entropy was applied to optimize parameters of phase space reconstruction, and disadvantages of traditional algorithms were overcome clearly. The computational accuracy of LE was improved greatly by using the HQ rule to calculate the number of neighbouring points. Simulation results showed that the improved small-data method here has good performances in estimating the largest Lyapunov exponent,and the algorithm is robust to noise.