Dynamics of neural networks with a central element

A neural network is considered which is designed as a system of phase oscillators and contains a central oscillator that interacts with a number of peripheral oscillators. Analytical and simulation methods are used to study the dynamics of the system that is conditioned by the interaction parameters and natural frequencies of the oscillators. The boundaries of parameter regions are found that correspond to the synchronization of the whole network or to partial synchronization between the central oscillator and a group of peripheral oscillators. For a system with two peripheral oscillators the bifurcation analysis is applied to describe the changes of synchronization modes. The implications of the results for attention modeling are discussed.