Synchronization in Coupled Map Lattices with Periodic Boundary Condition

We consider a lattice of coupled logistic maps with periodic boundary condition. We prove that synchronization and almost synchronization occur for the case of 1D lattice with lattice size n = 2, 3, 4 provided the coupling strength c is chosen in a suitable open interval contained in [0, 12 ]. For the case of lattice size n ≥ 4, we also show the numerical results of (almost) synchronized chaotic behavior of the coupled map lattice. For each fixed parameter γ ∈ [3.57, 4] of the logistic maps, the lattice sizes and the ranges of the coupling strengths c so that the coupled map lattice is synchronized, are given.