Spatial periodic synchronization of chaos in coupled ring and linear arrays of chaotic systems

Dynamic behaviors of coupled ring and linear arrays of unidirectionally coupled Lorenz oscillators are studied numerically. It is found that the chaotic rotating waves generated from the ring propagate with spatial periodic synchronization along the linear array, that is to say, two chaotic oscillators in the linear array are synchronized if the number of oscillators (spatial distance) between them is a multiple of oscillator number in the ring. Numerically it is shown that the stabilities of the synchronized states are enhanced by chaos, and degraded when the oscillators are far from the ring.