Shunting Inhibitory Cellular Neural Networks: Derivation and Stability Analysis

In this paper, a class of biologically inspired cellular neural networks is introduced. These networks possess lateral interactions of the shunting inhibitory type only; hence, they are called shunting inhibitory cellular neural networks (SICNN’s). Their derivation and biophysical interpretation are presented in this article, along with a stability analysis of their dynamics. In particular, it is shown that the SICNN’s are bounded input bounded output stable dynamical systems. Furthermore, a global Liapunov function is derived for symmetric SICNN’s. Using LaSalle invariance principle, it is shown that each trajectory converges to a set of equilibrium points; this set consists of a unique equilibrium point if all inputs have the same polarity.