# The Role of Topology in the Synchronization of Neuronal Networks Based on the Hodgkin-Huxley Model

## TL;DR

This study explores how different network topologies influence neuronal synchronization using Hodgkin-Huxley models, revealing that small-world structures enhance coherence and that inhibitory neurons decrease synchronization.

## Contribution

It introduces a detailed analysis of the impact of topology and neuron types on neural synchronization, including the effects of rewiring and degree distribution in Hodgkin-Huxley networks.

## Key findings

- Synchronization peaks in small-world networks.
- Inhibitory neurons reduce overall coherence.
- Synchronization follows a power-law distribution with network size.

## Abstract

Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon that can be seen in the brain. The network topology has a remarkable impact on both the function and the dynamics of neural networks. In this research, synchronization of neural networks is scrutinized through creating various topologies. These networks include both excitatory and inhibitory neurons. We investigate the dynamics of different networks by random rewiring of the synaptic connections. In this manner, a regular network transforms into a small-world network and then becomes a random network. Coherence level which is measured and utilized as the criteria to analyze synchronicity, experiencing a sharp increase as the network changes into the small-world network and growing steadily by the end. On the other hand, a decreasing trend of coherence level is revealed starting from a complete excitatory network and gradually increasing of inhibitory neurons. Thus, the coherence level reaches approximately zero in a complete inhibitory network. By increasing the number of neurons in the network, the degree of synchronization follows a power-law distribution; however, the number of synaptic connections of each neuron and their conductance have a positive impact on synchronization. By applying the model to a C-elegance neural network, not only the mentioned parameters but also the role of the degree distribution are highlighted.