Chaotic synchronization in lattices of two-variable maps coupled with one variable

Abstract

In this paper, we study chaotic synchronization in 1D lattices of two-variable maps coupled with one variable. We give a rigourous proof for the occurrence of chaotic synchronization of spatially homogeneous solutions in such coupled map lattices (CMLs) of lattice size n = 4 with suitable coupling coefficients. For the case of lattice size n > 4, we demonstrate numerical results of synchronized chaotic behaviour of the CMLs. Moreover, we show numerically that the difference between two variables manifests chaotic behaviour. This behaviour combined with the special coupling method in the CMLs guarantees high security in applications using our new model.