Edge of spatio-temporal chaos in cellular nonlinear networks

We investigate phenomena of the edge of spatially uniform chaotic mode and spatial temporal chaos in a lattice of chaotic 1D maps with only local connections. It is shown that in autonomous lattice with local connections, spatially uniform chaotic mode cannot exist if the Lyapunov exponent λ of the isolated chaotic map is greater than some critical value λ_cr>0. We proposed a model of a lattice with a pacemaker and found a spatially uniform mode synchronous with the pacemaker, as well as a spatially uniform mode different from the pacemaker mode