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; Nat. Comm. 15, 4955 (2024)

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.