1. ABOUT THE DATASET -------------------- Title: Sofia B. S. D. Castro, Claire M. Postlethwaite and Alastair M. Rucklidge (2025): Dataset for ``Visibility of heteroclinic networks''. https://doi.org/10.5518/1494 Creator(s): Sofia B. S. D. Castro [1], Claire M. Postlethwaite [2] and Alastair M. Rucklidge [3] Organisation(s): [1] Centro de Matematica and Faculdade de Economia, Universidade do Porto, Portugal. [2] Department of Mathematics, University of Auckland, New Zealand. [3] School of Mathematics, University of Leeds, Leeds LS2 9JT. Rights-holder(s): Sofia B. S. D. Castro, Claire M. Postlethwaite and Alastair M. Rucklidge Publication Year: 2025 Description: This the data (and the python scripts that generate the data) used in Figures 2 and 4-7 in the paper ``Visibility of heteroclinic networks'' by Sofia B. S. D. Castro, Claire M. Postlethwaite and Alastair M. Rucklidge. The paper is available on https://doi.org/10.48550/arXiv.2503.03440 There are 24 files in this dataset: x1x2x3_gh.py -- a Python script that generates x1x2x3_gh_output_?.txt (2 files) These data files contain the timeseries of two runs of the Guckenheimer--Holmes example differential equations with different initial conditions. x1x2x3x4_ks.py -- a Python script that generates x1x2x3x4_ks_output_?.txt (4 files) These data files contain the timeseries of four runs of the Kirk--Silber example differential equations with different parameter values and initial conditions. x1x2x3x4x5_rpssl_1D_2D_manifolds.py -- a Python script that generates x1x2x3x4x5_rpssl_1D_2D_manifolds_output_?.txt (10 files) These data files contain the timeseries of ten runs of the Rock--Paper--Scissors--Spock--Lizard example differential equations with different initial conditions. x1x2x3x4x5_rpssl.py -- a Python script that generates x1x2x3x4x5_rpssl_output_?.txt (4 files) These data files contain the timeseries of four runs of the Rock--Paper--Scissors--Spock--Lizard example differential equations with different parameter values and initial conditions. Cite as: Sofia B. S. D. Castro, Claire M. Postlethwaire and Alastair M. Rucklidge (2025), Dataset for ``Visibility of heteroclinic networks'', University of Leeds. https://doi.org/10.5518/1652 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 --------------- 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 ---------------------------------- Title: Centro de Matematica da Universidade do Porto Dates: Jan 2020 - Dec 2024 Funding organisation: Fundacao para a Ciencia e a Tecnologia Grant no.: UIDB/00144/2020 and UIDP/00144/2020 Title: Beyond survival of the fittest: population dynamics of cyclic competition networks Dates: Mar 2022 - Nov 2026 Funding organisation: Marsden Fund Council from New Zealand Government funding, managed by the Royal Society Te Aparangi Grant no.: 21-UOA-048 Title: DMS-EPSRC Eco-Evolutionary Dynamics of Fluctuating Populations Dates: Dec 2021 - May 2025 Funding organisation: EPSRC Grant no.: EP/V014439/1 4. CONTENTS ----------- File listing There are four python scripts: x1x2x3_gh.py x1x2x3x4_ks.py x1x2x3x4x5_rpssl_1D_2D_manifolds.py x1x2x3x4x5_rpssl.py Running the four python scripts will regenerate all the other data files. The data files have several lines of comments giving the parameter values of the runs and the headings for the columns. The data file names all have an index that gives the parameter values or initial conditions. The columns are (for x1x2x3_gh_output_?.txt): 1 time 2--4 log base 10 of the three x_i coordinates, i=1,2,3 5--7 the three x_i coordinates, i=1,2,3 This data was used for Figure 2 in the paper. The columns are (for x1x2x3x4_ks_output_?.txt): 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 This data was used for Figures 4 and 5 in the paper. The columns are (for x1x2x3x4x5_rpssl_1D_2D_manifolds_output_?.txt): 1--3 the x2, x4 and x1 coordinates 4--5 the two components of the pentacle projection defined in the paper 6--7 the same as 4--5 but rotated 1*2pi/5 8--9 the same as 4--5 but rotated 2*2pi/5 10--11 the same as 4--5 but rotated 3*2pi/5 12--13 the same as 4--5 but rotated 4*2pi/5 This data was used for Figure 6 in the paper. The columns are (for x1x2x3x4x5_rpssl_output_?.txt): 1 time 2--6 log base 10 of the five x_i coordinates, i=1,2,3,4,5 7--11 the five x_i coordinates, i=1,2,3,4,5 12--13 the two components of the pentacle projection defined in the paper This data was used for Figure 7 in the paper. 5. METHODS ---------- The dataset was generated by solving the ordinary differential equations given in the paper using the Python SciPy library solve_ivp: solve_ivp(dxdt, [0,tmax], initial_condition, method='RK45', rtol=1e-12, atol=1e-12, max_step=0.1)