Chaotic synchronization in lattice of partial-state coupled Lorenz equations

In this paper, we study chaotic synchronization in lattices of coupled Lorenz equations with Neumann or periodic boundary condition. Three different coupling configurations in the single xi-, yi- or zi-component are considered. Synchronization is affected by coupling rules. We prove that synchronization occurs for either xi- or yi-component coupling provided the coupling coefficient is sufficiently large. Moreover, we determine the dependence of coupling coefficients on the lattice size. For the case of the zi-component coupling, we demonstrate by numerical experience that the synchronization cannot occur.