1. ABOUT THE DATASET
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Title: Sofia B. S. D. Castro and Alastair M. Rucklidge (2024): Dataset for ``Robust heteroclinic cycles in pluridimensions''.
https://doi.org/10.5518/1494

Creator(s): Sofia B. S. D. Castro [1] and Alastair M. Rucklidge [2]

Organisation(s):
[1] Centro de Matematica and Faculdade de Economia, Universidade do Porto, Portugal.
[2] School of Mathematics, University of Leeds, Leeds LS2 9JT.

Rights-holder(s): Sofia B. S. D. Castro and Alastair M. Rucklidge

Publication Year: 2024

Description: There are 17 files in this dataset:
x1x2x3x4.py -- a Python program that generates all the other data files
eight files of the form:
 x1x2x3x4_output_?_?.txt. which contain the timeseries of eight runs (four cases and two parameter sets each) of the differential equations with different parameter values
eight files of the form:
 x1x2x3x4_light_gray_?_?.txt, which contain the stability information about the heteroclinic cycle.

Cite as: 

Sofia B. S. D. Castro and Alastair M. Rucklidge (2024), Dataset for ``Robust heteroclinic cycles in pluridimensions'', University of Leeds. https://doi.org/10.5518/1494

Related publication: 

Sofia B. S. D. Castro and Alastair M. Rucklidge (2024), ``Robust heteroclinic cycles in pluridimensions'' (Submitted).

Contact: 
Alastair Rucklidge A.M.Rucklidge@leeds.ac.uk

2. TERMS OF USE
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Unless otherwise stated, this dataset is licensed under a Creative Commons Attribution 4.0 International Licence: https://creativecommons.org/licenses/by/4.0/.]

3. PROJECT AND FUNDING INFORMATION
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Title: DMS-EPSRC Eco-Evolutionary Dynamics of Fluctuating Populations

Dates: Dec 21 - May 25

Funding organisation: EPSRC

Grant no.: EP/V014439/1

4. CONTENTS
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File listing

Python code that generates all the data: x1x2x3x4.py -- running this will regenerate all the other data files.

Eight files of the form x1x2x3x4_output_?_?.txt where the two numbers give the case number (1, 2, 3, 4) and the paramter set number (1,2).
These files were used to generate the last four figures in the paper.

The files have 17 lines of comments giving the parameter values of the runs and the headings for the columns.

The columns are:
 1    time
 2--5 log base 10 of the four x_i coordinates, i=1,2,3,4
 6--9 the four x_i coordinates, i=1,2,3,4

Eight files of the form x1x2x3x4_light_gray_?_?.txt where the two numbers give the case number (1, 2, 3, 4) and the paramter set number (1,2).
These demonstrate that the behaviour agrees with the calculated prediction and are included in the last four figures in the paper.

The files have four lines of comments giving the parameter values of the runs and the headings for the columns.

The columns are:
 1    time
 2    log base 10 of x4  


5. METHODS
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The dataset was generated by solving the ordinary differential equations using the Python SciPy library solve_ivp:

solve_ivp(dxdt, [0,tmax], initial_condition, method='RK45', rtol=1e-12, atol=1e-12, max_step=1.0)