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Shunting inhibitory cellular neural networks: derivation and stability analysis

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2 Author(s)
Bouzerdoum, A. ; Dept. of Electr. Eng., Adelaide Univ., SA, Australia ; Pinter, R.B.

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

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Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on  (Volume:40 ,  Issue: 3 )