Kuramoto oscillators on directed networks with negative binomial degree distributions

This repository contains C implementations of Kuramoto oscillators on networks generated using a negative binomial configuration model. The code supports parallel execution using OpenMP and flexible parameter input through command-line options.

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Features

• Generates directed networks with tunable heterogeneity using the negative binomial configuration model.
• Simulates Kuramoto oscillators with transient and total time steps.
• Supports varying either the coupling strength (K) or the average degree (avg_k) over a range of values.
• Parallelized using OpenMP for faster computation of multiple independent realizations.
• Command-line interface with default parameters and optional overrides.
• Outputs matrices of order parameters for each experiment.

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Files

File	Description
KuramotoDirectedNB.c	Main simulation code with parameter parsing and parallel execution.
nb_kuramoto.c / nb_kuramoto.h	Functions to generate the negative binomial configuration model and integrate Kuramoto's equations.
README.md	This documentation.

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Compilation

Serial version

gcc -o kur_dir KuramotoDirectedNB.c nb_kuramoto.c -ligraph -lgsl -lgslcblas -lm

Parallel version

gcc -fopenmp -o kur_dir KuramotoDirectedNB_with_function.c nb_kuramoto.c -ligraph -lgsl -lgslcblas -lm

Usage

./kur_dir [options]

Available options

Option	Description	Default
--dt <val>	Time step	0.01
--ttot <val>	Total simulation time	100
--ttrans <val>	Transient time	50
--N <val>	Number of nodes	100
--alpha <val>	Network heterogeneity	1.0
--avg_k <val>	Average degree	4.0
--K <val>	Coupling strength	3.5
--start_param <val>	Start of parameter range	2.0
--end_param <val>	End of parameter range	5.0
--num_params <val>	Number of parameter values	10
--num_experiments <val>	Number of experiments per param	30
--vary_coupling <0/1>	1 = vary K, 0 = vary avg_k	1
--help	Show help message	-

Output

• The program outputs a .dat file containing the results of all experiments for each parameter value. The first column corresponds to the varied parameter (avg_k or K), and the second column contains the corresponding order parameter. The data is organized in row-major order, with each row representing a single experiment for a specific parameter value.
• File naming depends on which parameter is varied (K or avg_k).

Example

# Vary coupling strength
./kur_dir --vary_coupling 1 --num_params 5 --num_experiments 10

# Vary average degree
./kur_dir --vary_coupling 0 --start_param 2 --end_param 8 --num_params 7