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Shunting Inhibitory Cellular Neural Networks: Derivation and Stability Analysis

Journal Article


Abstract


  • 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. �� 1993 IEEE

Publication Date


  • 1993

Citation


  • Bouzerdoum, A., & Pinter, R. B. (1993). Shunting Inhibitory Cellular Neural Networks: Derivation and Stability Analysis. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 40(3), 215-221. doi:10.1109/81.222804

Scopus Eid


  • 2-s2.0-0027568891

Start Page


  • 215

End Page


  • 221

Volume


  • 40

Issue


  • 3

Place Of Publication


Abstract


  • 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. �� 1993 IEEE

Publication Date


  • 1993

Citation


  • Bouzerdoum, A., & Pinter, R. B. (1993). Shunting Inhibitory Cellular Neural Networks: Derivation and Stability Analysis. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 40(3), 215-221. doi:10.1109/81.222804

Scopus Eid


  • 2-s2.0-0027568891

Start Page


  • 215

End Page


  • 221

Volume


  • 40

Issue


  • 3

Place Of Publication