Synchronization in an oscillator neural network model with time-delayed coupling

Abstract

We study collective synchronization in a neural network model of phase oscillators with time-delayed coupling. The network contains a central oscillator and peripheral oscillators which interact via the central oscillator. The introduction of delays in connections between elements of the network significantly changes the network dynamics. It is shown that, under certain conditions for the delays and coupling strengths, the network has a multitude of synchronization frequencies in contrast to the case without delays where it has, at most, one frequency. The coexistence of different synchronous states with their own basins of attraction is the characteristic property of the network with time-delayed coupling. The criteria for the existence of synchronous states and their stability are derived. Analysis of the asymptotic behaviour of the network under increasing connection strengths (K) and delays (τ) has shown that the number of synchronous regimes in the network is increasing, and even when tau is a small value the network still has several synchronous regimes (if K is large enough). The application of the main results to attention modelling is discussed.