Neuronal heterogeneity, characterized by multitude of spiking neuronal patterns, is a widespread phenomenon throughout the nervous system. In particular, the brain exhibits strong variability among inhibitory neurons. Despite the huge neuronal heterogeneity across brain regions, which in principle could decrease synchronization due to differences in intrinsic neuronal properties, cortical areas coherently oscillate during various cognitive tasks. Therefore, the functional
significance of neuronal heterogeneity remains a subject of active investigation. Previous studies typically focus on the role of heterogeneity in the dynamic properties of only one population. Here, we explore how different types of inhibitory neurons can contribute to the diversity of the phase relations between two cortical areas. This research sheds light on the potential impact of local properties, such as neuronal variability, on communication between distant
brain regions. We show that both homogeneous and heterogeneous inhibitory networks can exhibit phase diversity and nonintuitive regimes such as anticipated synchronization (AS) and phase bistability. It has been proposed that the bistable phase could be related to bi-stable perception, such as in the Necker cube, where the brain alternates between two interpretations of a static image. Moreover, we show that heterogeneity enlarges the region of zero-lag synchronization and bistability. We also demonstrate that the parameter controlling inhibitory heterogeneity modulates the transition from the usual delayed synchronization regime (DS) to AS. Finally, we show that inhibitory heterogeneity drives the internal dynamics of the free-running population. Therefore, we suggest a possible mechanism to explain when the DS-AS transition occurs via zero-lag synchronization or bi-stability.