The paper discusses the spatio-temporal phenomena in autonomous two-layer Cellular Neural Networks (CNNs) with mutually coupled templates between two layers. By computer calculations, we show how pattern formations, autowaves and classical waves can be regenerated in the networks, and describe the properties of these phenomena in detail. In particular, we focus our discussion on the necessary conditions for generating these spatio-temporal phenomena. In addition, the influences of the template parameters and initial state conditions of CNNs on the spatio-temporal phenomena are investigated.

This paper presents an algorithm for fingerprint image restoration using Digital Reaction-Diffusion System (DRDS). The DRDS is a model of a discrete-time discrete-space nonlinear reaction-diffusion dynamical system, which is useful for generating biological textures, patterns and structures. This paper focuses on the design of a fingerprint restoration algorithm that combines (i) a ridge orientation estimation technique using an iterative coarse-to-fine processing strategy and (ii) an adaptive DRDS having a capability of enhancing low-quality fingerprint images using the estimated ridge orientation. The phase-only image matching technique is employed for evaluating the similarity between an original fingerprint image and a restored image. The proposed algorithm may be useful for person identification applications using fingerprint images.

This paper presents a digital reaction-diffusion system (DRDS)--a model of a discrete-time discrete-space reaction-diffusion dynamical system--for designing new image processing algorithms inspired by biological pattern formation phenomena. The original idea is based on the Turing's model of pattern formation which is widely known in mathematical biology. We first show that the Turing's morphogenesis can be understood by analyzing the pattern forming property of the DRDS within the framework of multidimensional digital signal processing theory. This paper also describes the design of an adaptive DRDS for image processing tasks, such as enhancement and restoration of fingerprint images.

This paper explores a possibility of constructing massively parallel molecular computing systems using molecular electronic devices called enzyme transistors. The enzyme transistor is, in a sense, an artificial catalyst which selects a specific substrate molecule and transforms it into a specific product. Using this primitive function, various active continuous media for signal transfer/processing can be realized. Prominent examples discussed in this paper are: (i) Turing pattern formation and (ii) excitable wave propagation in a two-dimensional enzyme transistor array. This paper demonstrates the potential of enzyme transistors for creating reaction-diffusion dynamics that performs useful computations in a massively parallel fashion.

Numerical studies of reaction–diffusion systems which consist of chaotic oscillators are carried out. The Rössler oscillators are used, which are arranged two–dimensionally and coupled by diffusion. Pacemakers where the average periods of the oscillators are artificially changed are set to produce target patterns. It is found that target patterns emerge from pacemakers and grow up as if they were in a regular oscillatory medium. The wavelength of the pattern can be varied and controlled by changing the parameters (size and frequency) of the pacemaker. The behavior of the coupled system depends on the size of the system and the strength of the pacemaker. When the system size is large, the Poincar return maps show that the behavior of the coupled system is not simple and the orbit falls into a high–dimensional attractor, while for a small system the attractor is rather simple and a one–dimensional map is obtained. Moreover, for appropriate strength of pacemakers and for certain sizes of the systems the oscillations become periodic. It is also found that the largest and local Lyapunov exponents of the system are positive and these values are uniformly distributed over the pattern. The values of the exponents are smaller than that of the uncoupled Rössler oscillator; this is due to the fact that the diffusion reduces the exponents and modifies the form of the attractor. We conclude that the large scale patterns can stably exist in the chaotic medium.