The Research Of Cellular Neural Networks With Trapezoidal And Impulsive Activation Function

Cellular Neural Network(CNN),originated from Hopfield's neural net-work and Neumann's cellular automata,is a continuous,parallel informa-tion processing system.As a class of non-linear dynamical system,CNN shows complex dynamical properties.Also,as a new pattern of logical computation,CNN possesses powerful computation capability.In this thesis,a class of cellular neural network(CNN)with trapezoidal activation function(CNNwTAF)is investigated.With theα-z plane parti-tioned into 25 disjoint open regions,where parameters a and z respectively stand for the output synaptic weight and system threshold,the stationary solutions of CNNwTAFs are discussed with some useful results obtained. Moreover,for a special kind of CNNwTAF,the sufficient conditions of the existence of Smale's horseshoe induced by the stationary solutions' maps are studied,which in part implies the complexity of the maps.CNNwIAF,namely,a cellular neural network(CNN)scheme employ-ing a new non-linear output function,called the impulsive,activation func-tion(IAF),is presented in the thesis.Combining with some interesting properties of the offset levels of CNN with respect to input vectors,it is shown that theoretically any non-separable Boolean function can be re-alized by using only one single-layer CNN.Specially,in the case of a one-dimensional CNN,a few appropriate IAFs are adopted and a novel inverse offset level method is used as the design of the CNN template.Fur-thermore,it is shown that XOR and NXOR Boolean operations with two inputs and all 152 non-separable Boolean functions with three inputs are easily implemented by a single CNNwIAF.Finally,the entire set of 152 CNN templates associated with 152 non-separable Boolean functions with three inputs is completely determined.For the famous game-of-life which is a linearly non-separable Boolean function with 9 inputs,the template of realizing the Boolean function by a single CNNwIAF is also given.