On stability of full range and polynomial type CNNs

Cellular neural networks (CNNs) are analog dynamic processors that have found several applications for the solution of complex computational problems. The mathematical model of a CNN consists in a large set of coupled nonlinear differential equations that have been mainly studied through numerical simulations; the knowledge of the dynamic behavior is essential for developing rigorous design methods and for establishing new applications. In most applications (such as image processing tasks) it is required that the CNN be stable, i.e. that after a transient all the trajectories tend to a constant value (with at most the exception of a set of measure zero). So far, three main CNN models have been proposed: the original Chua-Yang model, the full range model, that was exploited for VLSI implementation and the polynomial type model, which presents polynomial interactions among the cells. This manuscript is devoted to the study of the stability properties of polynomial type CNNs and to the comparison of such properties with those of Chua-Yang and of full range models.