The Topologic Entropy Of The Stationary Solution's Map Of Cellular Nonlinear Networks

Cellular Nonlinear Networks also called Cellular Neural Networks (CNN), is a new type of networks proposed by Chua and Yang in 1988. It is a partial linking dynamical system which is based on some charateristics of globally linking networks and the locally interactive characteristic of cell automata.The CNN has been implemented in virtually all existing CNN silicon chips and has many applications, It has broad applications in image and video signal processing, robotic and biological visions, higher brain functions and so on. With the deepening researches on Cellular Nonlinear Networks and chaos, great progresses have been made in the theoretical and applied researches on chaotic phenomena in CNN. Since it has very complex dynamical behavior, the understanding of the pattern formation or spatial properties of CNN is far from perfection.As a kind of topological conjugate invariant, the topologic entropy can perfectly describe complex behavior of dynamical system. Therefore it plays a very important role in the study of dynamical system. In this paper, topologic entropy will be employed to study the dynamical behavior of one-dimensional CNN, especially, the iteration map of stationary solution of CNN.The CNN with based-term will be restudieiin Chapter 3. Under certain parameters, the stationary solutions' iteration map is topological conjugate to a Beruonulli shift of certain symbolic space. Moreover, the spatial entropy function of the map is two-dimensional and can be obtained explicitly as a space devil-staircase.