Fourier analysis of a delayed Rulkov neuron network

•We characterize the dynamics of the neurons and neuron networks from their behaviors in frequency domain by using Fourier analysis.•We analyze the synchronization of a delayed neuron network using signal analysis tools.•We develop an algorithm that allows computing the particular delay that synchronizes the network.•This algorithm is robust when we introduce a parametric noise in the neurons. We have analyzed the synchronization of some different networks 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. 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.