Stability of CNN with trapezoidal activation function

Bilgili E., Goknar I. C., Ucan O. N., Albora M.

International Symposium on Complex Computing-Networks, İstanbul, Turkey, 13 - 14 June 2005, vol.104, pp.225-227 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 104
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.225-227
  • Istanbul University Affiliated: Yes


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.