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
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
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.