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SWoNs

OVERVIEW

This repository contains code for the project "Synchronizing to Decide in Small-World Networks" from the 2018 Summer School in Computational Sensory-Motor Neuroscience (CoSMo 2018).

This code allows you to generate and test network connectivity structures applied to decision making tasks. Networks are generated using Rudolph-Lilith and Muller's method for small-world directed graphs [1], along with implementation details from Watts and Strogatz's 1998 paper on small-world networks [2]. By varying Rudolph-Lilith and Muller's rewiring proportion, q - analgous to Watts and Strogatz's rewiring probability p, networks can be produced along the continuum of ring lattice --> small world network --> random network.

A ring lattice network. N = 10, k = 2, q = 0.05.

A small-world network. N = 10, k = 2, q = 0.05.

A random network. N = 10, k = 2, q = 0.05.

FILE STRUCTURE

The structure of the files is as follows:

Initalization Files

  • createNetwork.m
    • networkStats.m
      • characteristicPathLength.m
      • clusteringCoefficient.m
    • generateRandomNetwork.m
  • createEnvironment.m

Oscillator Files

  • To be completed.

Simulation Scripts

  • To be completed.

REFERENCES

[1] Michelle Rudolph-Lilith and Lyle E. Muller. Algebraic approach to small-world network models. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 89(1):1–8, 2014.

[2] Duncan J. Watts and Steven H. Strogatz. Collective dynamics of ’small-world’ net- works. Nature, 393(6684):440–442, 1998.

NOTE: This code has been tested on MATLAB 2018a.