  Anticipated synchronization (AS) is a counter intuitive behavior that has
been observed in several systems. When AS establishes in a sender-receiver
configuration, the latter can predict the future dynamics of the former for
certain parameter values. In particular, in neuroscience AS was proposed to
explain the apparent discrepancy between information flow and time lag in the
cortical activity recorded in monkeys. Despite its success, a clear
understanding on the mechanisms yielding AS in neuronal circuits is still
missing. Here we use the well-known phase-resetting-curve (PRC) approach to
study the prototypical sender-receiver-interneuron neuronal motif. Our aim is
to better understand how the transitions between delayed to anticipated
synchronization and anticipated synchronization to phase-drift regimes occur.
We construct a map based on the PRC method to predict the phase-locking regimes
and their stability. We find that a PRC function of two variables, accounting
simultaneously for the inputs from sender and interneuron into the receiver, is
essential to reproduce the numerical results obtained using a Hodgkin-Huxley
model for the neurons. On the contrary, the typical approximation that
considers a sum of two independent single-variable PRCs fails for intermediate
to high values of the inhibitory connectivity between interneuron. In
particular, it looses the delayed-synchronization to
anticipated-synchronization transition.
