The effect of the excitatory feedback in anticipated synchronization and phase bistability regimes in neuronal populations

Abstract

Anticipated synchronization (AS), in which the receiver leads the sender and the phase lag is negative, can emerge in unidirectionally coupled dynamical systems when the receiver has faster internal dynamics than the sender. In cortical-like population models, AS and bistability between AS and delayed synchronization (DS) have been reported mainly in unidirectional motifs and have been proposed as possible explanations for phase relations observed in electrophysiological recordings. Because cortical areas are often connected bidirectionally, it is important to understand how excitatory feedback from the receiver to the sender affects the emergence and persistence of anticipatory synchronization and phase-bistable regimes. Here, we investigate the effect of the excitatory feedback on the phase relations between two cortical-like neuronal populations. We show that AS and phase bistability are not restricted to strictly unidirectional architectures, but remain robust in the presence of reciprocal coupling. In addition, we find that the transition from AS to DS can occur through different routes within the same motif, either via a bistable regime or via zero-lag synchronization, depending on the inhibitory coupling. More generally, the model exhibits a rich repertoire of phase relations, including: positive, negative, and zero-lag phase-lockings, as well as phase bistability, and phase-drift regimes. These results are consistent with the diversity of phase relations reported in electrophysiological experiments and suggest that fixed structural connectivity may support rapid reconfiguration of functional dynamics without requiring structural rewiring.