Effects of network structure and node dynamics on synchronization with time delays

Abstract

The synchronization behavior of neuronal networks is central to the functionality of the nervous system and is influenced by factors such as network topology, node dynamics, and time delays. This study investigates the impact of time delays on the synchronization behavior of chemically synaptic coupled neuronal networks, with a focus on analyzing changes in synchronization stability under different time delays and their underlying mechanisms. Through master stability function (MSF) analysis, we found that only networks with homogeneous degrees possess the same synchronization manifold, and can achieve stable synchronization under appropriate time delays. Numerical simulation results indicate that heterogeneous networks can also synchronize under suitable delays. By combining phase response curve (PRC) analysis with node dynamics, we revealed that different phase stimuli lead to variations in the firing periods of nodes in the network, and these periods changes are key to whether the network can synchronize under time delay. The comparison between neuronal firing characteristics and PRC values further confirmed this conclusion. These findings provide theoretical support for understanding the synchronization mechanisms in neural networks and offer new insights into synchronization disorders in neurological diseases.