  Several experiments and models have highlighted the importance of neuronal
heterogeneity in brain dynamics and function. However, how such a cell-to-cell
diversity can affect cortical computation, synchronization, and neuronal
communication is still under debate. Previous studies have focused on the
effect of neuronal heterogeneity in one neuronal population. Here we are
specifically interested in the effect of neuronal variability on the phase
relations between two populations, which can be related to different cortical
communication hypotheses. It has been recently shown that two spiking neuron
populations unidirectionally connected in a sender-receiver configuration can
exhibit anticipated synchronization (AS), which is characterized by a negative
phase-lag. This phenomenon has been reported in electrophysiological data of
non-human primates and human EEG during a visual discrimination cognitive task.
In experiments, the unidirectional coupling could be accessed by Granger
causality and can be accompanied by both positive or negative phase difference
between cortical areas. Here we propose a model of two coupled populations in
which the neuronal heterogeneity can determine the dynamical relation between
the sender and the receiver and can reproduce phase relations reported in
experiments. Depending on the distribution of parameters characterizing the
neuronal firing patterns, the system can exhibit both AS and the usual delayed
synchronization regime (DS, with positive phase) as well as a zero-lag
synchronization regime and phase bistability between AS and DS. Furthermore, we
show that our network can present diversity in their phase relations
maintaining the excitation-inhibition balance.
