... Email: chaos@mail.cplire.ru . ... We investigate phenomena on the edge of spatially homogeneous chaotic mode and spatiotemporal chaos in a lattice of chaotic 1-D maps with local connections. We show that spatially homogeneous chaotic mode cannot exist in a lattice with local connections if the Lyapunov exponent of the isolated chaotic map is greater than some critical positive value. We propose a few schemes that make spatial synchronization possible in large lattices. ...