Self-regulation of a network of Kuramoto oscillators

Abstract

Persistent global synchronization of a neuronal network is considered a pathological, undesired state. Such as synchronization is often caused by the loss of neurons that regulate network dynamics, or cells that assist these neurons such as glial cells. Here we propose a self-regulation model in the framework of complex networks in which we assume that, for sake of simplicity, glial cells prevent the over synchronization of the neuronal network. We have considered a brain-like network characterized by a modular organization combined with a dynamic description of the nodes as Kuramoto oscillators. We have applied a self-regulation mechanism to keep local synchronization while avoiding global synchronization at the same time. To do so, we have added self-regulation to the system by switching off for a certain period of time a selection of edges that link nodes showing a synchronization above a certain threshold. Despite the simplicity of the approximation, our results show that it is possible to maintain a high local synchronization (module level) while keeping low the global one. In addition, characteristic dynamic patterns have been observed when analysing synchronization between modules in large modular networks. Our work could help to understand the effects of localized regulatory actions on modular systems with synchronous phenomena, such as neuroscience and other fields.