耦合Lorenz模型的吸引子特性及其可预报性分析  

Analysis of Attractor Behavior and Predictability in a Coupled Lorenz Model

作　　者：张铭 王伟[1] 钟权加[2] 丁瑞强[1,3] 李建平 ZHANG Ming;WANG Wei;ZHONG Quanjia;DING Ruiqiang;LI Jianping(Plateau Atmosphere and Environment Key Laboratory of Sichuan Province,Chengdu University of Information Technology,Chengdu 610225;State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics(LASG),Institute of Atmospheric Physics,Chinese Academy of Sciences,Beijing 100029;State Key Laboratory of Earth Surface Processes and Resource Ecology,Beijing Normal University,Beijing 100875;Key Laboratory of Physical Oceanography of the Ministry of Education,Ocean University of China,Qingdao 266100)

机构地区：[1]成都信息工程大学四川省高原大气与环境重点实验室,成都610225 [2]中国科学院大气物理研究所大气科学和地球流体力学数值模拟国家重点实验室,北京100029 [3]北京师范大学地表过程与资源生态国家重点实验室,北京100875 [4]中国海洋大学物理海洋教育部重点实验室,青岛266100

出　　处：《大气科学》2023年第6期1746-1756,共11页Chinese Journal of Atmospheric Sciences

基　　金：国家自然科学基金项目42225501,42105059。

摘　　要：通过改变耦合Lorenz模型中控制快、慢子系统之间耦合强度的参数,本文探究了耦合强度对该系统的混沌吸引子特性及可预报性的影响。结果表明:随着耦合增强,快系统中显示出与慢系统类似的低频变化特征,其吸引子也随之变大;而慢系统高频分量变大,导致其变率增强,吸引子轨道变得更加密集。在此基础上,利用非线性局部Lyapunov指数方法定量分析了耦合强度对耦合Lorenz系统可预报性的影响。具体来说,在耦合之后,耦合系统的对数误差增长曲线包含前后两段不同的误差增长率,分别代表快速和慢速误差增长过程。此外,各子系统的可预报性对耦合强度变化响应并不一致,随着对快系统的耦合强度增加,快/慢两个不同尺度系统的可预报上限均减少。然而,增加对慢系统的耦合强度却只能提高快系统的可预报上限,对慢系统的可预报性改变不大。This paper investigates the implications of the coupling strengths on chaotic attractors and the predictability by varying the parameters controlling the coupling strengths of the fast and slow dynamics in a coupled Lorenz system.The results show that as the strengths of the coupling increase,low-frequency variations similar to those of the slow dynamics can be found in the fast dynamics;moreover,its attractor becomes larger.In addition,the high-frequency variability of the slow dynamics increases,leading to the enhancement of its variability and denser attractor orbits.Herein,the effects of the coupling strengths on predictability of the coupled Lorenz model are quantified using the nonlinear local Lyapunov exponent method.The results demonstrate that after coupling,the natural logarithm curves of the error growth of the coupled dynamics comprise two distinct growth rates,where the first and second periods depict fast and slow error growth processes,respectively.Furthermore,the predictability of sub-dynamics responds differently to variations in the coupling strengths.Increasing coupling strengths in the fast dynamics reduces the predictability limit for both fast and slow dynamics.However,strengthening the coupling to the slow dynamics solely heightens the fast dynamics’predictability limit without significantly altering the predictability of the slow dynamics.

关 键 词：非线性局部Lyapunov指数(NLLE) 耦合Lorenz系统 误差增长 可预报性 

分 类 号：P456[天文地球—大气科学及气象学]