In this paper, we present an analytical design approach for the class of bipolar cellular neural networks (CNN's) which yields optimally robust template parameters. We give a rigorous definition of absolute and relative robustness and show that all well-defined CNN tasks are characterized by a finite set of linear and homogeneous inequalities. This system of inequalities can be analytically solved for the most robust template by simple matrix algebra. For the relative robustness of a task, a theoretical upper bound exists and is easily derived, whereas the absolute robustness can be arbitrarily increased by template scaling. A series of examples demonstrates the simplicity and broad applicability of the proposed method.

: In this paper the basic structure and features of SCNN 2000, a universal simulation system for Cellular Neural Networks (CNN) is presented. Since the rst presentation of SCNN [1] the structure of the simulation system has been changed to achieve more exibility in simulating CNN. Especially, a wider class of training algorithms including new optimization methods have been implemented. SCNN 2000 also supports several kinds of CNN hardware as mathematical coprocessors. Additionally, a new SCNN control system has been developed, including a new graphical user interface and an integrated SCNN shell to allow a more convenient working with SCNN 2000. In this part of the contribution the basic structure and features of SCNN 2000 will be discussed, whereas the SCNN control system is presented in a second paper [2]. 1. Introduction Since it's rst presentation in [1] SCNN 1 has become one of the mostly used simulation systems for CNN [3]. It operates under dierent systems, like AIX-UNIX,...

A learning algorithm based on the decomposition of the A-template into symmetric and anti-symmetric parts is introduced. The performance of the algorithm is investigated in particular for coupled CNNs exhibiting diffusion-like and propagating behavior. 1. INTRODUCTION Cellular neural networks (CNNs) are examples of recurrent networks defined by the following system of differential equations dx ij (t) dt =-x ij (t) + # mn#N ij amn y mn (t) + # mn#N ij bmn u mn + I , where N ij denotes the neighborhood of the ij-th cell for 1 # i # M,1# j # N and y = (|x +1|-|x -1|)/2 . The state, input and output of a cell are defined by x ij , u ij and y ij , respectively. We assume a nearest neighborhood CNN. The output at an equilibrium point, when one exists, is denoted by y # ij .The parameters of a CNN are gathered into the so-called A-template, the B-template and the bias I. In view of learning algorithms, since a CNN is a recurrent neural network, one can apply the lea...

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This paper describes a solution proposal for automatically tuning cellular neural network--- CNN templates for given CNN Universal Machine --- CNN-UM chips in order to make them respond in the same fashion as a simulator, i.e. to minimize or even eliminate the erroneous behavior of actual CNN-UM chips. The approach uses measurements of actual CNN-UM chips as part of the cost function for the adaptive simulated annealing---ASA algorithm to find an optimal template given an initial approximation, e.g. a template used for a simulator. The tuned templates are therefore customized versions that are expected to be much less sensitive to imperfections on the manufacturing process and other reasons of erroneous behavior of CNN-UM chips. Results are presented for the binary and gray scale input cases. The automatic tuning was able to find better templates for all considered tasks. It is expected that the maturity of this technique will give to CNN-UM chips enough reliability to compete with digital systems in terms of robustness in addition to advantages in speed.