Phase Synchronization in Phase Oscillators and a Complex-Valued Neural Network and Its Applications to Traffic Flow Control

Abstract

Phase synchronization property of the coupled system of oscillatory units are utilized for the offset control of the traffic signals. 2 systems are numerically compared; one is the coupled system of the phase oscillators with a pair-wise sinusoidal interaction, and the other is a specific type of a complex-valued Hopfield neural network which possesses the network energy function. The dynamics of the latter system is decomposable into the dynamics of the amplitude and phase of each neuron, and the dynamics of phase is equivalent to the former system with the modified coupling strength. The numerical calculation shows that both systems give the similar offset values for the simple traffic patterns. However for the relatively large and complicated traffic conditions, the neural network shows the advantage of the convergence to the synchronized state while the oscillator system sometimes fails.