Anticipated synchronization in neuronal network motifs

Abstract

Two identical dynamical systems coupled unidirectionally (in a so called master-slave configuration) exhibit anticipated synchronization (AS) if the one which receives the coupling (the slave) also receives a negative delayed self-feedback. In oscillatory neuronal systems AS is characterized by a phase-locking with negative time delay τ between the spikes of the master and of the slave (slave fires before the master), while in the usual delayed synchronization (DS) regime τ is positive (slave fires after the master). A 3-neuron motif in which the slave self-feedback is replaced by a feedback loop mediated by an interneuron can exhibits both AS and DS regimes. Here we show that AS is robust in the presence of noise in a 3 Hodgkin-Huxley type neuronal motif. We also show that AS is stable for large values of τ in a chain of connected slaves-interneurons.