README FILE


#### REPOSITORY OVERVIEW

This repository contains the .ode files used to generate the numerical data underlying the figures in the associated paper. 
The files implement both full network models and their corresponding phase-difference reductions for different neuronal systems.



#### SOFTWARE

To run the simulations and reproduce the data:

- XPPAUT : Required for numerical simulations and data generation
- MATLAB (optional) : Used for figure creation and visualization
- XPPLORE (optional) : Alternative tool for visualization



#### ORGANIZATION

The repository is organised as follows.

1 - FHN: Folder containing the .ode file associated with the network and phase-difference model of FHN neurons.
2 - ML : Folder containing the .ode file associated with the network and phase-difference model of ML neurons.
3 - MF : Folder containing the .ode file associated with the network and phase-difference model of neural mass models.

Each folder contains different files.

- *_network.ode  : Network model.
- *_phase.ode    : Phase-difference model.
- *_H_Table.table: Table associated to the interaction function H.



#### FIGUREs

The following files were used to generate the data presented in each figure of the paper.


- Figure 1: Delay-induced slow modulation of spiking activity in the FHN model with delay parameter eta = 0.08.
    * `FHN3_network.ode`
    * `FHN3_phase.ode`

- Figure 2: Bifurcation analysis of the phase-difference model associated with the network of FHN neurons. (eta in [0, 0.15])
    * `FHN3_phase.ode`

- Figure 3: Bifurcation analysis of the phase-difference model associated with the network of FHN neurons. (eta in [0.13, 0.30])
    * `FHN3_phase.ode`

- Figure 4: Bifurcation diagram and phase-plane analysis for the FHN phase-difference model for larger delays. (eta in [0.63, 0.66])
    * `FHN3_phase.ode`

- Figure 5: Slow modulation in larger networks of FHN oscillators.
    * `FHN5_network.ode`
    * `FHN5_phase.ode`
    * `FHN7_network.ode`
    * `FHN7_phase.ode`
    * `FHN9_network.ode`
    * `FHN9_phase.ode`

- Figure 6: Slow modulation in a network of Morris-Lecar neurons with delayed, inhibitory coupling.
    * `ML3_network.ode`
    * `ML3_phase.ode`

- Figure 7: Bifurcation analysis of the phase-difference model corresponding to the Morris-Lecar model. (eta in [0.10, 0.30])
    * `ML3_phase.ode`

- Figure 8: Bifurcation analysis of the phase-difference model corresponding to the Morris-Lecar model. (eta in [0.65, 0.80])
    * `ML3_phase.ode`

- Figure 9: Slow modulation of the next-generation mean-field model. 
    * `MF3_network.ode`
    * `MF3_phase.ode`

- Figure 10: Bifurcation analysis of the phase-difference model corresponding to the mean-field model. (eta in [0.40, 0.50])
    * `MF3_phase.ode`

- Figure 11: Bifurcation analysis of the phase-difference model corresponding to the mean-field model. (eta in [0.80, 0.90])
    * `MF3_phase.ode`

- Figure 12: The period of the slow modulation is lower with larger coupling strengths.
	**** CHANGES IN THE .ode FILEs ARE REQUIRED ****
    * `ML3_network.ode`
    * `ML3_phase.ode`
    * `MF3_network.ode`
    * `MF3_phase.ode`

- Figure 13: Slow modulation in an asymmetric FHN network with delays only in the bidirectional coupling between 1 and 2.
	**** CHANGES IN THE .ode FILEs ARE REQUIRED ****
    * `FHN3_network.ode`
    * `FHN3_phase.ode`



#### AUTHORs

Xinxin Qie (1,*)
Matteo Martin (2,*) 
Shenquan Liu (1) ~ Corresponding author
Morten Gram Pedersen (2,3) ~ Lead corresponding author

(*) Both authors contributed equally to the work.
(1) School of Mathematics, South China University of Technology
(2) Department of Information Engineering, University of Padova
(3) Padova Neuroscience Center, University of Padova



#### CONTACTs

Corresponding author: Shenquan Liu ~ mashqliu@scut.edu.cn
Lead corresponding author: Morten Gram Pedersen ~ mortengram.pedersen@unipd.it