Neuronal activity in the brain exhibits a synchronized pattern during restful states and a desynchronized pattern during active behaviors. Synaptic plasticity during the synchronized states is critical for knowledge reorganization and abstraction. However, the mechanisms underlying the influence of synchronized neuronal activity on neural circuits through plasticity remain incompletely understood. The transition between synchronized and desynchronized states involves substantial modulation of inhibition, which significantly alters the excitation-inhibition (EI) balance in synaptic inputs. The Kuramoto model is commonly used to study the collective synchronization of oscillators, including neurons. In this study, we introduced the EI-Kuramoto model, a variant of the Kuramoto model. The model organizes oscillators into excitatory and inhibitory groups, defining each by distinct interaction strengths in four interaction types. In numerical simulations and theoretical analysis, we identified three types of dynamics through numerical simulations: synchronized, bistable, and desynchronized. These states are manipulable via adjustments in the four interaction strengths. Furthermore, we developed the model by incorporating plasticity, resulting in the plastic EI-Kuramoto (pEI-Kuramoto) model. Models with high inhibitory strength exhibited a desynchronized order parameter and consistent connection strength. In contrast, models with low inhibition showed fluctuating order parameters and connection strengths, particularly in connections of medium strength. The strongest connections remained stable. These findings suggest that stabilizing a selected number of strong connections might promote knowledge reorganization and abstraction. Our results illuminate how variations in EI balance impact network stability and coupling, providing deeper insights into synaptic networks and the process of knowledge reshaping.