BİLGİLİ, E., GÖKNAR, İ.C., UÇAN, O.N. (2005). Cellular neural network with trapezoidal activation function. International Journal of Circuit Theory and Applications, Volume 33, Issue 5, pp. 393-417.
This paper presents a cellular neural network (CNN) scheme employing a new non-linear activation function, called trapezoidal activation function (TAF). The new CNN structure can classify linearly non-separable data points and realize Boolean operations (including eXclusive OR) 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. By processing several examples of synthetic images, the analytically derived stability condition is also confirmed.