Finite-Time Recurrence Network Transitivity in the Ergodic Limiter Tokamak Map

This repository contains the numerical simulation codebase associated with the manuscript "Finite-Time Recurrence Network Transitivity in the Ergodic Limiter Tokamak Map" by Matheus S. Palmero and Reik V. Donner. The core of the project models and analyzes the Ullmann Map (an Ergodic Limiter Tokamak Map). The code is primarily written in C and is designed to calculate phase spaces, track time series, search for periodic orbits, and compute recurrence transitivity and network properties for the system. Repository Structure The repository is structured to separate the core mathematical functions, the main simulation execution, and the generated data/visualizations: ullmann_map_main.c: The main execution script that binds the simulation tools and map functions together. manuscript.pdf: The associated research paper detailing the theoretical foundations, methodology, and results of this study. Functions/: Contains the core C modules for the numerical analysis. ullmann_map.c & ullmann_manifolds.c: Definitions and manifold calculations specific to the Ullmann Map. transitivity.c & recurrence.c: Modules to compute finite-time recurrence and transitivity metrics. phase_space.c, time_series.c, discrete_space.c: Functions to track trajectories and evolve initial conditions. periodic_orbit_search.c: Tools for identifying unstable periodic orbits (UPOs). Tools/: Contains auxiliary mathematical solvers (e.g., Gauss, Newton-Raphson) and matrix operations. data/: Stores the output files, initial conditions, and plotting scripts. *.dat: Output data files (e.g., phase spaces, transitivity tests). *.sh (e.g., plot_transitivity.sh, plot_phase_spaces.sh): Shell scripts that use Gnuplot to generate visualizations from the simulation data. figs_test/ & phase_spaces/: Directories containing generated .png plots and phase space outputs. General Idea The purpose of this code is to investigate chaotic transport and topological features of the Ergodic Limiter Tokamak Map. By utilizing finite-time recurrence networks, the simulation evaluates the transitivity of the system to identify distinct dynamical regimes and structural properties of the phase space. Requirements C Compiler: GCC or equivalent to compile the C scripts. Gnuplot: Required to run the .sh scripts in the data/ folder for plotting and visualizing the output data.