Fourier analysis of a delayed Rulkov neuron network

Abstract

We have analyzed the synchronization of some different networks of chaotic Rulkov neu- rons 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 net- work when it was slightly synchronized, or to get synchronized when it was desynchro- nized. 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. The algorithm has been applied for two well-known network models: the small-world and Erdös-Rényi. We have also tested the algorithm by using non-homogeneous neurons affected with a parametric noise.