# Fourier analysis of a delayed Rulkov neuron network

## TL;DR

This paper uses Fourier and wavelet analysis to study synchronization in a delayed, chaotic Rulkov neuron network, developing an algorithm to optimize delay for improved synchronization.

## Contribution

It introduces a novel Fourier-based algorithm to optimize delay in a neuron network, enhancing synchronization in chaotic, small-world networks.

## Key findings

- Algorithm improves synchronization with optimal delay
- Fourier and wavelet transforms characterize neuron behavior
- Robustness tested with noisy, non-homogeneous neurons

## Abstract

We have analyzed the synchronization of a small-world network of chaotic Rulkov neurons with an electrical coupling that contains a delay. We have developed an algorithm to compute a certain delay whose result is to improve the synchronization of the network when it was slightly synchronized, or to get synchronized when it was desynchronized. Our general approach has been to use tools from signal analysis, such as Fourier and wavelet transforms. With these tools, we have characterized the behavior of the neurons for different parameters in frequency and time-frequency domains. Finally, the robustness of the algorithm has been tested by using non-homogeneous neurons affected with a parametric noise.