Lorenz System Simulation Dataset

<pre><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 </pre><pre><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. </pre><pre><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.</pre><pre><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. </pre><pre><b> Additional information: </b> <b>For additional information about the datasets, check the !INFO!.png file</b> <img> !INFO!.png </img></pre>