clustersynchronization's Introduction

Cluster Synchronization Errors in Julia

This is the repository hosting some basic scripts and data used in the papers

"Endowing networks with desired symmetries and modular behavior". P. Khanra, S. Ghosh, D. Aleja, K. Alfaro-Bittner, G. Contreras-Aso, R. Criado, M. Romance, S. Boccaletti, P. Pal, and C. Hens; Phys. Rev. E 108, 054309 (2023).
"The transition to synchronization of networked systems". A. Bayani, F. Nazarimehr, S. Jafari, K. Kovalenko, G. Contreras-Aso, K. Alfaro-Bittner, R.J. Sánchez-Garcı́a, and S. Boccaletti; arXiv:2303.08668

General information

The repository is structured as follows:

Folder SynchronizationErrors contains the scripts necessary for computing the cluster synchronization errors of a given dynamical system over a given network. They are written in Julia using some basic scientific libraries (DifferentialEquations, MAT, LinearAlgebra, Statistics...) and making use of multithreading, parallelizing the solver with a different value of the coupling per thread.
- The ClusterSynchErrors-*.jl scripts can be modified with the desired dynamical system and network, and then run.
- The class*dynamics.jl contains a collection of possible dynamical systems to consider, already formatted appropriately.
- To automatize running the Julia script over and over again, the batch_senders.sh bash file can be run using
```
nohup ./batch_senders.sh &
```
Folder Input contains adjacency and/or Laplacian matrices of some networks, as well as initial conditions (close to the respective attractors).
The data files in Data_all_simulations contain the already pre-processed (averaged) values of the synchronization errors per cluster of each simulation shown in the aforementioned papers.
Folder LyapunovExpCalculation contains scripts which can be run to compute the Master Stability Function (maximum Lyapunov exponent) of a given dynamical system, along with examples of them.

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