[PDF] Top 20 On the spatial entropy and patterns of two-dimensional cellular neural networks

... formations of two-dimensional standard cellular neural networks (CNN) as well as the complexity of the binary ...patterns. The complexity is ... See full document

... GENERATION AND SPATIAL ENTROPY IN TWO-DIMENSIONAL LATTICE MODELS ∗ JUNG-CHAO BAN † , SONG-SUN LIN ‡ , AND YIN-HENG LIN § ...Abstract. Patterns generation problems in ... See full document

... a and ε approximately, say (z, a) ∈ [5, 1] ε , where aε < 0 (see Theorem ...3.5 of [Juang & Lin, 2000]), we see, via Lemma 4.1 of [Juang & Lin, 2000], that any positively saturated cell, de- noted by ... See full document

... three-dimensional patterns generation problems and its ap- plications to three-dimensional Cellular Neural ...for the set of all local patterns is ... See full document

... partitioning the parameter space into finite many disjoint ...classification of the set of mosaic patterns in each region. The lower spatial entropy bound of ... See full document

... rest of this paper is organized as follows. Section 2 derives the reduction operator C m which can recursively reduce higher order elementary patterns to lower ...Then, the lower-bound ... See full document

... problems and their applications to three-dimensional Cellular Neural Networks ...for the set of all local patterns is established to derive a recursive formula for ... See full document

... investigates the complexity of the global set of output patterns for one-dimensional multi-layer cellular neural networks with ...to the output space ... See full document

... studies on lattice dynamical systems to further ...treating the problems of allocating the parameters with which the considered system exhibits de- sirable patterns or some ... See full document

... elucidates the dense entropy of two-dimensional inhomogeneous cellular neural networks (ICNN) with/without ...to the learning problem (or inverse problem); ... See full document

... 0, and c 1 ∈ R is a biased term. The graph of F is given in ...1. The motivation for studying such a map is, in part, due to the form of the map is a gen- eralized version ... See full document

... physical and mathematical backgrounds of CNNs as well as their applications, we refer to [Chua, 1998; Chua & Roska, 1993; Chua & Yang, 1988a, 1988b; Crounse et ...Much of the theoretical work ... See full document

... describes the spatial disorder of one-dimensional Cellular Neural Networks (CNN) with a biased term by applying the iteration map ...parameters, the map is ... See full document

... that the existence of basic patterns can be determined for each parameter ...region. The mosaic patterns can then be completely characterized through formulating suitable transition ... See full document

... one-dimensional Cellular Neural Network with an output function which is nonflat at ...infinity. Spatial chaotic regions are completely characterized. Moreover, each of their exact ... See full document

... investigation of two-layer CNNs can be extended to decoupling a MCNN into k ...decouple the solution space Y. Suppose Y is the solution space of a three-layer ...into two spaces, ... See full document

... existence of the Smale-Horseshoe of a corresponding two-dimensional ...profile of stationary traveling wave solutions of a discrete analog of one-dimensional ... See full document

... In the architecture of cellular neural networks (CNN), connections among cells are built on linear coupling ...by the so-called templates which express the local ... See full document

... investigates the relations between subspaces of the solution space of a multi-layer cellular neural ...modification of the above procedure allows for decoupling ... See full document

... A) of Poincar´ e map are computed. In many interesting cases, including the ZN-case, finitely many chaotic andwindow regions interweave with each ...regions, the largest Lyapunov exponent is positive ... See full document