双月刊

ISSN 1006-9895

CN 11-1768/O4

耦合Lorenz模型的吸引子特性及其可预报性分析
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作者单位:

1.成都信息工程大学, 四川省高原大气与环境重点实验室;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;3.北京师范大学, 地表过程与资源生态国家重点实验室;4.中国海洋大学,物理海洋教育部重点实验室, 青岛

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基金项目:

国家自然科学基金41975070、42105059


Analysis of attractor behavior and predictability in a coupled Lorenz model
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Affiliation:

1.Plateau Atmosphere and Environment Key Laboratory of Sichuan Province, Chengdu University of Information Technology;2.State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing;3.State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University;4.Key Laboratory of Physical Oceanography.MOE.China, Ocean University of China,Qingdao,China

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    摘要:

    本文主要探究了耦合Lorenz系统的混沌吸引子特性及其可预报性随耦合强度的变化特征。结果表明:随着耦合强度增加,快系统中的低频变化分量增大,其吸引子也随之变大;而慢系统自身的不稳定分量变大,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(NLLE)方法定量分析了耦合系数变化对耦合Lorenz系统可预报性的影响。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性都会减少。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。

    Abstract:

    There are many complex multi-scale systems in real life. Studying these coupled systems can help us to gain a more comprehensive understanding of the dynamical properties of the systems. In this paper, the implications of coupling strength on chaotic attractors and their predictability are investigated by varying the coupling coefficients of a coupled Lorenz model, which combined with a fast and slow dynamics. The results show that as the coupling coefficient increases, similar low-frequency variations to those of the slow dynamics can be found in the fast dynamics, along with its attractor becoming larger; while the high-frequency variability of the slow dynamics increases. The predictability limits of the system are investigated using the nonlinear local Lyapunov exponent (NLLE) method. It is found that after coupling, the natural logarithm curves of error growth of both the fast and slow dynamics consist of two distinct growth rates, with the first period being the fast error growth and the second period being the slow error growth process. Furthermore, the saturation value of the error growth varies from the strength of the coupling. However, the sensitivity to the coupling coefficient is not the same for the predictability of systems of different scales. Increasing the coupling coefficient leads to a larger attractor for the fast dynamics, providing more predictable information, which offsets the effect of a reduction in the predictability limit due to the increased error growth rate, ultimately leading to a longer predictability time for the fast system. However, for the slow dynamic system, the size of the chaotic attractor is minimally affected by the strength of the coupling, but an increase in the coupling coefficient will significantly add the instability of the slow dynamics, thus reducing the predictability limit of the slow system. Finally, this study can provide new insights into the predictability of such complex climate systems.

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历史
  • 收稿日期:2021-12-09
  • 最后修改日期:2022-02-08
  • 录用日期:2022-06-20
  • 在线发布日期: 2022-06-21
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