Stability of CNN with trapezoidal activation function
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CitationBİLGİLİ E. GÖKNAR, İ.C., UÇAN, O.N., ALBORA, A.M. (2006). Stability of CNN with trapezoidal activation function. Springer Proceedings in Physics. (Editor İ.C. GÖKNAR, L. SEVGİ) pp. 225-233, Berlin, Springer. http://dx.doi.org/110.1007/3-540-30636-6_25
This paper presents the stability conditions of cellular neural network (CNN) scheme employing a new nonlinear activation function, called trapezoidal activation function (TAF). The new CNN structure can classify linearly nonseparable data points and realize Boolean operations (including XOR) by using only a single-layer CNN. In order to simplify the stability analysis, a feedback matrix W is defined as a function of the feedback template A and 2D equations are converted to 1D equations. The stability conditions of CNN with TAF are investigated and a sufficient condition for the existence of a unique equilibrium and global asymptotic stability is derived.