Small Amplitude, Phase Locked Response in Oscillatory Networks with Delays

The global dynamics of an artificial neural network composed by oscillators with delays is investigated. Using center manifold reduction and normal form theory, the equation governing the whole network dynamics is reduced to an amplitude-phase model (i.e. a set of coupled differential equations describing the evolution of both the amplitudes and the phases of the oscillators). The analysis of a network with a simple architecture reveals that different kind of phase locked oscillations is admissible, and the possible coexistence of in-phase and anti-phase locked solutions.