BioMath-Public-Goods-Dilemma

PDE Model for Public Goods Dilemma

This repository contains the simulation codes, LaTeX source files of the paper, and the generated figures.
The goal is to reproduce and analyze the spatial public goods dilemma models in both one and two dimensions.

Contents

LaTeX files

The full draft of the paper, including all equations and references.

• main.tex: Main LaTeX file.
• references.bib: All references.

Simulation notebooks and scripts

Figures in the paper are generated by the simulation codes in this repository.

• threshold_values_unbiased.py: Generates Figure 1.
• dispersion_relations.py and Turing_region_unbiased.py: Generate Figure 2 in the paper.
• threshold_values_biased.py: Generates Figure 3 in the paper.
• dispersion_relations.py and Turing_region_biased.py: Generate Figure 4 in the paper.
• bifurcation_unbiased.py: Generates Figure 5 in the paper.
• pitchfork_bifurcation.py: Generates Figure 6 in the paper.
• bifurcation_biased.py: Generates Figure 7 in the paper.
• equilibrium_r_u, equilibrium_mu_u: Generate Figure 8 in the paper.
• extra_ru_unbiased, extra_ru_biased, extra_mu_u_unbiased and extra_mu_u_biased: Generate Figure 9 in the paper.
• unbiased_random_initial_conditions_simulations.m: Generates Figure 10 in the paper.
• unbiased_approximation.m: Generates Figure 11 in the paper.
• turing_instability.m: Generates Figure 12 in the paper.
• biased_random_initial_conditions_simulations.m: Generates Figure 13 in the paper.
• biased_approximation.m: Generates Figure 14 in the paper.
• bifurcation_unbiased.py and bifurcation_biased.py: Generate Figure 15 in the paper.
• extra_ru_unbiased, extra_ru_biased, extra_mu_u_unbiased and extra_mu_u_biased: Generate Figure 16 in the paper.
• D_v_public_goods.m and w_u_public_goods.m: Generate Figure 17 in the paper.
• unbiased_snapshot.m and biased_snapshot.m: Generate Figure 18 in the paper.