Simultaneous and sequential synchronisation in arrays

We discuss the possibility of simultaneous and sequential synchronisation in vertical and horizontal arrays of unidirectionally coupled discrete systems. This is realized for the specific case of two dimensional Gumowski-Mira maps. The synchronised state can be periodic, thereby bringing in control of chaos, or chaotic for carefully chosen parameters of the participating units. The synchronised chaotic state is further characterised using variation of the time of synchronisation with coupling coefficient, size of the array, etc. In the case of the horizontal array, the total time of synchronisation can be controlled by increasing the coupling coefficient step wise in small bunch of units