The analytic criteria are presented for the local activity theory in two-port Cellular Neural Network (CNN) cells with three local state variables, and the application to a Biochemical Model CNN (BMCNN) is given for coupling in series of two enzymes whose prototype was studied by Decroly and Goldbeter. The bifurcation diagrams of the BMCNN's show that there does not exist a locally passive domain, and the computer simulation exhibited that convergent patterns, oscillatory patterns or chaotic patterns may emerge if the selected cell parameters are located in locally active unstable domains but nearby the edge of chaos domain. In particular, the coexistence of multiple oscillations was observed in the corresponding triple cell couples of the BMCNN's with the same initial conditions.