Determining the Spectrum of the Nonlinear Local Lyapunov Exponents in a Multidimensional Chaotic System  

作　　者：Ruiqiang DING Jianping LI Baosheng LI 

机构地区：[1]State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics,Institute of Atmospheric Physics,Chinese Academy of Sciences [2]Plateau Atmosphere and Environment Key Laboratory of Sichuan Province,Chengdu University of Information Technology [3]College of Global Change and Earth System Sciences,Beijing Normal University [4]University of Chinese Academy of Sciences

出　　处：《Advances in Atmospheric Sciences》2017年第9期1027-1034,共8页大气科学进展（英文版）

基　　金：supported by the National Natural Science Foundation of China for Excellent Young Scholars (Grant No. 41522502);the National Program on Global Change and Air–Sea Interaction (Grant No. GASI-IPOVAI06);the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant No. 2015BAC03B07)

摘　　要：For an n-dimensional chaotic system, we extend the definition of the nonlinear local Lyapunov exponent （NLLE） from one- to n-dimensional spectra, and present a method for computing the NLLE spectrum. The method is tested on three chaotic systems with different complexity. The results indicate that the NLLE spectrum realistically characterizes the growth rates of initial error vectors along different directions from the linear to nonlinear phases of error growth. This represents an improvement over the traditional Lyapunov exponent spectrum, which only characterizes the error growth rates during the linear phase of error growth. In addition, because the NLLE spectrum can effectively separate the slowly and rapidly growing perturbations, it is shown to be more suitable for estimating the predictability of chaotic systems, as compared to the traditional Lyapunov exponent spectrum.For an n-dimensional chaotic system, we extend the definition of the nonlinear local Lyapunov exponent （NLLE） from one- to n-dimensional spectra, and present a method for computing the NLLE spectrum. The method is tested on three chaotic systems with different complexity. The results indicate that the NLLE spectrum realistically characterizes the growth rates of initial error vectors along different directions from the linear to nonlinear phases of error growth. This represents an improvement over the traditional Lyapunov exponent spectrum, which only characterizes the error growth rates during the linear phase of error growth. In addition, because the NLLE spectrum can effectively separate the slowly and rapidly growing perturbations, it is shown to be more suitable for estimating the predictability of chaotic systems, as compared to the traditional Lyapunov exponent spectrum.

关 键 词：Lyapunov exponent nonlinear local Lyapunov exponent PREDICTABILITY 

分 类 号：P435[天文地球—大气科学及气象学]