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.

The chaotic synchronization in n-dimensional large map networks with local coupling and their size stabilities in the node number N-->infinity are studied analytically and numerically. The analytical results show that the chaotic synchronization is stable for N-->infinity in the presence of the external driving or global coupling. The numerical calculations show that, as the driving or global interaction strength increases from zero, the network states have the whole route: spatiotemporal chaotic state --> cluster chaotic synchronous state --> complete chaotic synchronous state --> spatiotemporal pattern --> spatiotemporal chaotic state.