Self-regulation of a network of Kuramoto oscillators

Persistent global synchronization within a neuronal network is generally considered an undesirable, pathological state that often arises from to the loss of regulatory neurons or associated glial cells. In this study, we introduce a self-regulation model based on complex networks, simplified to represent glial cells as inhibitory agents against network over-synchronization. We employ a modular network architecture and describe the dynamics of nodes using Kuramoto oscillators. Our model features a unique self-regulation mechanism designed to preserve local synchronization while minimizing global synchronization. This is achieved by temporarily disabling edges between nodes that exceed a predefined synchronization threshold. Despite the model's simplified view of glial roles in modulating neuronal dynamics, our results demonstrate the feasibility of maintaining high levels of local synchronization while suppressing the global one. Furthermore, we observe distinct dynamic patterns when examining inter-module correlations in modular networks. Our findings offer valuable insights into the localized regulatory actions on modular systems exhibiting synchronous behaviors, with implications extending beyond neuroscience to other complex systems.