Application of Local Activity Theory of CNN to the Coupled Cell Cycle Clock Model

Abstract

The local activity principle of the cellular nonlinear network (CNN) introduced by Chua([1]-[3]) has provided a powerful tool for studying the emergence of complex patterns in a homogeneous lattice formed by coupled cells. Based on the cell-cycle clock differential equation introduced by Presnov and Agur [4], this paper establishes a cell-cycle clock CNN system in aim to describe the actions among cyclins and active maturations promotion factors (MPF). Using the analytical criteria for the local activity of two-port CNN cells with three state variables [5] calculates the chaos edge of the cell-cycle clock CNN system . The numerical simulations show that the emergence may exist if the selected cell parameters are nearby the edge of chaos domain. The cell-cycle clock CNN can exhibit periodicity and chaos. These results demonstrate once again the effectiveness of the local activity theory in choosing the parameters for the emergence of complex patterns of CNNs.