Synchronization in a neural network model with time delayed coupling

Investigates a neural network model design as a system of peripheral oscillators with different natural frequencies interacting via the central oscillator. The oscillators interact with a time delay τ, corresponding to the finite velocity of signal propagation. The authors study the synchronization under various values of τ. It is shown that under some conditions for a finite delay time there exists a multitude of synchronization frequencies in contrast to the case without delay where the system has at most one solution. The criteria for multiple solutions existence and their stability are found. The asymptotic behaviour under increasing connection strengths is analyzed.