Synchronization in a neural network of phase oscillators

A neural network model is considered which is designed as a system of phase oscillators with different natural frequencies. The network contains a central oscillator and peripheral oscillators which interact via the central oscillator. The regime of partial synchronization was studied when current frequencies of the central oscillator and one group of peripheral oscillators are near to each other while current frequencies of other peripheral oscillators are far from being synchronized with the central oscillator. Approximation formulas for the average frequency of the central oscillator in the regime of partial synchronization are derived, and the results of computation experiments are presented which characterize the accuracy of the approximation. The interpretation of the results in terms of attention modeling is discussed.