Study of Collective Synchronous Dynamics in a Neural Network Model

A network with coupled biological neurons provides various forms of collective synchronous dynamics. Such phase-locking dynamics states resemble eigenvectors in a linear coupling system in that the forms are determined by the symmetry of the coupling strengths. However, the states behave as attractors in a nonlinear dynamics system. We here study the collective synchronous dynamics in a neural system by using a novel theory. We exhibit how the period and the stability of individual phase-locking dynamics states are determined by the characteristics of synaptic couplings. We find that, contrary to common sense, the firing rate of a synchronized state decreases with increasing synaptic coupling strength.