CAJ | 학술논문

针对常用的几种Lyapunov指数数值计算方法,即定义法、正交法、wolf法和小数据量法,以典型的Lorenz系统为例,分别计算Lorenz混沌吸引子的Lyapunov指数谱或者最大Lyapunov指数,比较各种方法的计算精度、计算复杂度,并且对含噪声的混沌时间序列给出Lyapunov指数计算结果,比较各种抗干扰能力.给出了不同计算方法的性能差异、适用场合和选择依据.
침대상용적궤충Lyapunov지수수치계산방법,즉정의법、정교법、wolf법화소수거량법,이전형적Lorenz계통위례,분별계산Lorenz혼돈흡인자적Lyapunov지수보혹자최대Lyapunov지수,비교각충방법적계산정도、계산복잡도,병차대함조성적혼돈시간서렬급출Lyapunov지수계산결과,비교각충항간우능력.급출료불동계산방법적성능차이、괄용장합화선택의거.
In this paper,the several computational methods of Lyapunov exponents are compared,i.e.,the definition method,the orthogonal method,the wolf method and the small data sets.The Lyapunov exponent power and the max-Lyapunov exponent are computed through the above methods for Lorenz system.From the results,the accuracies and the complexity of the above methods are investigated.Furthermore,the max-Lyapunov exponents are also calculated for the chaotic time series including the noise.Finally,numerical results demonstrate that the performances of different computational methods have differences,and some summaries will be presented.