Shunting inhibitory cellular neural networks: derivation and stability analysis

Abstract

A class of biologically inspired cellular neural networks (CNNs) is introduced that possess lateral interactions of the shunting inhibitory type only; hence, they are called shunting inhibitory cellular neural networks (SICNNs). Their derivation and biophysical interpretation are presented along with a stability analysis of their dynamics. In particular, it is shown that the SICNNs are bounded input bounded output stable dynamical systems. Furthermore, a global Lyapunov function is derived for symmetric SICNNs. Using the 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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>