One of the key features of Cellular Neural Networks (CNN) is the ability to perform high speed computation with memory storage localized to each cell. In this work we shall present a special class of hysteresis CNN with memristor synapses operating on the edge of chaos. In general, a spatially continuous or discrete medium made of identical cells interacting with all cells located within a neighborhood exhibits complexity if the homogeneous medium can give rise to a non-homogeneous state or spatio-temporal pattern under some homogeneous initial and boundary conditions. Throughout extensive simulations we shall present non-uniform spatial-pattern generation and we shall study the global motion of excitable waves.