sandor-battaglini-fischer / complex-system-simulation

Coupled linear ODEs to model relationship dynamics

Romantic Chaos: A study of the emergence of unpredictability in relationships

As part of the course "Complex System Simulation" - University of Amsterdam 2024 Used to support the final presentation of the project. This includes creating grpahs, visualizations and animations, as well as to get a deeper understanding of the model and the dynamics of the model.

License:

Overview

This repository contains Python scripts to create graphs for our final presentation. TO be able to run the scripts see the requirements below. By clicking on the run option in the .py file or running each cell in the .ipynb file, the graphs will be created.

File Descriptions

triangular.ipynb

This file includes the plots for the triangular relationships part.

external_stress.ipynb

external_stress.ipynb gives the plots for the base model and external stress models.

6d.ipynb

This file sets up basic plotting for the 6D dynamical system based on Sternberg's "Triangular Theory of Love"

love_dynamics.ipynb

Plotting of linear models and Gone with the Wind

Usage

These scripts were run with Python 3.11.0 on MacOS Ventura.

Requirements:

• matplotlib==3.7.1
• scipy==1.10.1
• networkx==3.1
• ipywidgets==8.0.4
• numpy==1.24.3
• pickle (in standard package)
• mpl_toolkits (in standard package)
• plotly==5.9.0
• pandas==1.5.3
• multiprocessing
• tqdm==4.65.0
• ipython==8.12.0
• time (in standard package)
• os (in standard package)
• unittest (in standard package)
• imageio==2.31.1
• PIL==10.2.0 (also called Pillow)
• matplotlib-inline==0.1.6

References:

The following material inspired and provided the equations and initial parameter values for our model:

• Rinaldi, S., Rossa, F. D., Dercole, F., Gragnani, A., & Landi, P. (2015). Modeling Love Dynamics: Vol. Volume 89. WORLD SCIENTIFIC. https://doi.org/10.1142/9656
• ERBAŞ, Kadir Can. “Modeling Love with 4D Dynamical System.” Chaos Theory and Applications, vol. 4, no. 3, Akif Akgul, 30 Nov. 2022, pp. 135–143. doi:10.51537/chaos.1131966.​
• Strogatz, S. H. (1988) Love affairs and differential equations. Math. Magazine 61, 35.
• N.V. Kuznetsov; G.A. Leonov (2005). "On stability by the first approximation for discrete systems". Proceedings. 2005 International Conference Physics and Control, 2005. Vol. Proceedings Volume 2005. pp. 596–599.
• G. A. Leonov; N.V. Kuznetsov (2007). "Time-Varying Linearization and the Perron effects". International Journal of Bifurcation and Chaos. 17 (4): 1079–1107.

Contact

[e-mail] [e-mail] [e-mail] [e-mail]

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Developed by Sándor Battaglini-Fischer, Yehui He, Thomas Norton, Victor Piaskowski