Lorenz System Simulation Dataset

Name: Lorenz System Simulation Dataset
Creator: Harvard Dataverse
Published: 2025-05-12 00:02:13
License: 暂无描述

DataCite Commons2025-05-12 更新2025-04-15 收录

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https://dataverse.harvard.edu/citation?persistentId=doi:10.7910/DVN/BKNNTK

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资源简介：

<pre> Lorenz system simulation: - Wiki: https://en.wikipedia.org/wiki/Lorenz_system - Original Article: https://journals.ametsoc.org/view/journals/atsc/20/2/1520-0469_1963_020_0130_dnf_2_0_co_2.xml - Tau sims: https://arxiv.org/pdf/2207.00521.pdf - Rho exp: https://arxiv.org/pdf/2207.00521.pdf - Rho sin: https://pubs.aip.org/aip/cha/article/31/3/033149/342213/Using-machine-learning-to-predict-statistical </pre> <pre> Terminology: - Time span or time range : duration of time over which the simulation runs. - Time step or delta time : incremental time interval the simulation progresses. - Initial conditions (IC) : initial values of the dependent variables and derivs. </pre> <pre> Data Generation: 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. </pre> <pre> File Information: Each CSV file contains a 2D array, mostly of the form: sim number, subsim number, t, x, y, z, rho or rho_0 value. The default Lorenz System parameters are sigma = 10, rho = 28 and beta = 8/3. The files where the parameters were changed are named with the parameters values. </pre> <pre> Additional information: For additional information about the datasets, check the !INFO!.png file <img> !INFO!.png </img> </pre>

洛伦兹系统（Lorenz system）仿真： - 维基百科（Wiki）: https://en.wikipedia.org/wiki/Lorenz_system - 原始论文（Original Article）: https://journals.ametsoc.org/view/journals/atsc/20/2/1520-0469_1963_020_0130_dnf_2_0_co_2.xml - Tau仿真（Tau sims）: https://arxiv.org/pdf/2207.00521.pdf - Rho实验（Rho exp）: https://arxiv.org/pdf/2207.00521.pdf - Rho正弦（Rho sin）: https://pubs.aip.org/aip/cha/article/31/3/033149/342213/Using-machine-learning-to-predict-statistical 术语定义： - 时间跨度或时长范围（Time span or time range）: 仿真运行的总时长。 - 时间步长或增量时间（Time step or delta time）: 仿真推进的增量时间间隔。 - 初始条件（Initial Conditions, IC）: 因变量及其导数的初始取值。 数据生成方式： 本数据集通过MATLAB生成，即采用ODE45求解器进行多步积分。ODE45求解器实现了变步长龙格-库塔（Runge-Kutta）方法以提升计算效率。每场仿真均采用[0, 1]区间内的随机初始条件，单场仿真的时间跨度为1至100，时间步长设为0.01。 文件信息： 每个CSV文件包含一个二维数组，其标准格式为：仿真编号、子仿真编号、时间t、变量x、y、z、ρ（rho）或ρ₀（rho_0）值。洛伦兹系统的默认参数为σ（sigma）=10，ρ（rho）=28，β（beta）=8/3。修改了系统参数的文件会以对应参数值命名。 附加说明： 如需了解该数据集的更多详情，请查看!INFO!.png文件。 <img>!INFO!.png</img>

提供机构：

Harvard Dataverse

创建时间：

2024-09-11

搜集汇总

数据集介绍