SHUNTING INHIBITORY CELLULAR NEURAL NETWORKS - DERIVATION AND STABILITY ANALYSIS

In this paper, a class of biologically inspired cellular neural networ ks is introduced. These networks possess lateral interactions of the s hunting inhibitory type only; hence, they are called shunting inhibito ry cellular neural networks (SICNN's). Their derivation and biophysica l 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. Furtherm ore, a global Liapunov function is derived for symmetric SICNN's. Usin g LaSalle invariance principle, it is shown that each trajectory conve rges to a set of equilibrium points; this set consists of a unique equ ilibrium point if all inputs have the same polarity.