Abstract We have considered the complexity and asymptotic stability in the process of biochemical substance exchange in a coupled ring of cells. We have used coupled maps to model this process. It includes the coupling parameter, cell affinity and environmental factor as master parameters of the model. We have introduced: (i) the Lempel–Ziv complexity spectrum and (ii) the Lempel–Ziv complexity spectrum highest value to analyze the dynamics of two cell model. The asymptotic stability of this dynamical system using an eigenvalue-based method has been considered. Using these complexity measures we have noticed an “island” of low complexity in the space of the master parameters for the weak coupling. We have explored how stability of the equilibrium of the biochemical substance exchange in a multi-cell system (N=100) is influenced by the changes in the master parameters of the model for the weak and strong coupling. We have found that in highly chaotic conditions there exists space of master parameters for which the process of biochemical substance exchange in a coupled ring of cells is stable.