Nonlinear feedback-controlled generalized synchronization of spatial chaos

Consider the following two spatially generalized Logistic systems:xm+1,n+ωxm,n+1=1−μ1[(1+ω)xmn]2andym+1,n+ωym,n+1=1−μ2[(1+ω)ymn]2,where ω is a real constant, and μ1 and μ2 are two real parameters. An analytical method is introduced for generalized synchronization of these two spatially chaotic systems, and a range of the coupling constant is specified for the generalized synchronization. Moreover, a nonlinear function is characterized for synchronization stability of the two coupled systems.