基于MATLAB对于Lorenz-96系统的分析及可视化研究
Analysis and Visualization of the Lorenz \'96 System Based on MATLAB
程睿豪 1周明震1
作者信息
- 1. 西南大学物理科学与技术学院，重庆，400715
- 折叠
摘要
混沌系统由于其特性，目前在气象预测、加密通讯、信息安全以及新兴人工智能神经网络等方面有着极为广泛的应用。本文旨在使用MATLAB对于Lorenz96系统进行研究，探索不同的非线性强迫项对于洛伦兹96系统进行约束，以期对其他研究提供可用模型。并且给出集中不同的非线性强迫项约束下的可视化图像以及其在三维上的相空间投影，模拟出粒子在该种吸引子中的空间运动轨迹，从而阐明其特性。本研究建立的分析框架具有超越L96模型本身的普适性。该思路可直接推广至其他受迫耗散的偏微分方程系统,为探索"外部调控的函数形式与系统内在混沌特性间的映射关系"提供了一个可操作的研究路径。
Abstract
Due to their characteristics, chaotic systems are currently widely used in meteorological forecasting, encrypted communications, information security, and emerging artificial intelligence neural networks. This paper aims to study the Lorenz \'96 system using MATLAB, exploring the constraints imposed by different nonlinear forcing terms on the system, in order to provide usable models for other research. It also presents visualizations under several distinct nonlinear forcing terms, along with their three-dimensional phase space projections, simulating the spatial motion trajectories of particles within such attractors, thereby elucidating their characteristics. The analytical framework established in this study has universality that extends beyond the L96 model itself. This approach can be directly generalized to other forced-dissipative partial differential equation systems, providing an operable research pathway for exploring the mapping relationship between the functional form of external forcing and the intrinsic chaotic characteristics of the system.关键词
MATLAB/可视化/Lorenz96系统/非线性约束Key words
MATLAB/visualization/Lorenz \'96 system/nonlinear constraint引用本文复制引用
程睿豪,周明震.基于MATLAB对于Lorenz-96系统的分析及可视化研究[EB/OL].(2026-05-28)[2026-06-03].http://www.paper.edu.cn/releasepaper/content/202605-126.学科分类
物理学
