Lorenz System Simulation Dataset

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<b> Lorenz system simulation: </b>

- <b>Wiki</b>: https://en.wikipedia.org/wiki/Lorenz_system
- <b>Original Article</b>: https://journals.ametsoc.org/view/journals/atsc/20/2/1520-0469_1963_020_0130_dnf_2_0_co_2.xml
- <b>Tau sims</b>: https://arxiv.org/pdf/2207.00521.pdf
- <b>Rho exp</b>: https://arxiv.org/pdf/2207.00521.pdf
- <b>Rho sin</b>: https://pubs.aip.org/aip/cha/article/31/3/033149/342213/Using-machine-learning-to-predict-statistical
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<b>Terminology: </b>

- <b>Time span or time range </b>: duration of time over which the simulation runs.
- <b>Time step or delta time </b>: incremental time interval the simulation progresses.
-<b> Initial conditions (IC) </b>: initial values of the dependent variables and derivs.
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<b>Data Generation: </b>

The datasets are generated using MATLAB, i.e. utilizing the ODE45 solver with multi-step integration. The ODE45 solver function implements the Runge-Kutta method with a variable time step for efficient computations. Each simulation starts with random initial conditions in the range [0, 1]. The time span for each simulation ranges from 1 to 100 with a time step of 0.01.
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<b>File Information: </b>

Each CSV file contains a 2D array, mostly of the form:
<b>sim number, subsim number, t, x, y, z, rho or rho_0 value. </b>

The default Lorenz System parameters are <b>sigma = 10, rho = 28 and beta = 8/3. </b>
The files where the parameters were changed are named with the parameters values.
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<b> Additional information: </b>

<b>For additional information about the datasets, check the !INFO!.png file</b>
<img> !INFO!.png </img>
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搜集汇总

背景与挑战

背景概述

该数据集包含通过MATLAB ODE45求解器生成的Lorenz系统模拟数据，采用Runge-Kutta方法和变步长积分，数据以CSV格式存储，包含模拟参数和时间序列结果。默认系统参数为sigma=10, rho=28, beta=8/3，部分文件针对不同参数进行了调整。