Excitation–Inhibition Balance Controls Synchronization in a Simple Model of Coupled Phase Oscillators

Collective neuronal activity in the brain synchronizes during rest and desynchronizes during active behaviors, influencing cognitive processes such as memory consolidation, knowledge abstraction, and creative thinking. These states involve significant modulation of inhibition, which alters the excitation-inhibition (EI) balance of synaptic inputs. However, the influence of the EI balance on collective neuronal oscillation remains only partially understood. In this study, we introduce the EI-Kuramoto model, a modified version of the Kuramoto model, in which oscillators are categorized into excitatory and inhibitory groups with four distinct interaction types: excitatory-excitatory, excitatory-inhibitory, inhibitory-excitatory, and inhibitory-inhibitory. Numerical simulations identify three dynamic states-synchronized, bistable, and desynchronized-that can be controlled by adjusting the strength of the four interaction types. Theoretical analysis further demonstrates that the balance among these interactions plays a critical role in determining the dynamic states. This study provides valuable insights into the role of EI balance in synchronizing coupled oscillators and neurons.