Cellular Neural Network Cell Research Articles

Application of Local Activity Theory of Cellular Neural Network with Two Ports to the Coupled Lorenz-Cell Model**The project supported by National Natural Science Foundation of China under Grant No. 60074034 and the Foundation for University Key Teacher by the Ministry of Education of China

Some criteria for the local activity theory in two-port cellular neural network cells with three local state variables are applied to a coupled Lorenz-cell model. The numerical simulation exhibited that emergence may exist if the selected cell parameters are nearby or on the edge of chaos domain. The local activity theory has provided a new tool of studying the complexity of high dimensional coupled nonlinear physical systems.

MUTATIONS OF THE "GAME OF LIFE": A GENERALIZED CELLULAR AUTOMATA PERSPECTIVE OF COMPLEX ADAPTIVE SYSTEMS

This paper presents a novel approach for studying the relationship between the properties of isolated cells and the emergent behavior that occurs in cellular systems formed by coupling such cells. The novelty of our approach consists of a method for precisely partitioning the cell parameter space into subdomains via the failure boundaries of the piecewise-linear CNN (cellular neural network) cells [Dogaru & Chua, 1999a] of a generalized cellular automata [Chua, 1998]. Instead of exploring the rule space via statistically defined parameters (such as λ in [Langton, 1990]), or by conducting an exhaustive search over the entire set of all possible local Boolean functions, our approach consists of exploring a deterministically structured parameter space built around parameter points corresponding to "interesting" local Boolean logic functions. The well-known "Game of Life" [Berlekamp et al., 1982] cellular automata is reconsidered here to exemplify our approach and its advantages. Starting from a piecewise-linear representation of the classic Conway logic function called the "Game of Life", and by introducing two new cell parameters that are allowed to vary continuously over a specified domain, we are able to draw a "map-like" picture consisting of planar regions which cover the cell parameter space. A total of 148 subdomains and their failure boundaries are precisely identified and represented by colored paving stones in this mosaic picture (see Fig. 1), where each stone corresponds to a specific local Boolean function in cellular automata parlance. Except for the central "paving stone" representing the "Game of Life" Boolean function, all others are mutations uncovered by exploring the entire set of 148 subdomains and determining their dynamic behaviors. Some of these mutations lead to interesting, "artificial life"-like behavior where colonies of identical miniaturized patterns emerge and evolve from random initial conditions. To classify these emergent behaviors, we have introduced a nonhomogeneity measure, called cellular disorder measure, which was inspired by the local activity theory from [Chua, 1998]. Based on its temporal evolution, we are able to partition the cell parameter space into a class U "unstable-like" region, a class E "edge of chaos"-like region, and a class P "passive-like" region. The similarity with the "unstable", "edge of chaos" and "passive" domains defined precisely and applied to various reaction–diffusion CNN systems [Dogaru & Chua, 1998b, 1998c] opens interesting perspectives for extending the theory of local activity [Chua, 1998] to discrete-time cellular systems with nonlinear couplings. To demonstrate the potential of emergent computation in generalized cellular automata with cells designed from mutations of the "Game of Life", we present a nontrivial application of pattern detection and reconstruction from very noisy environments. In particular, our example demonstrates that patterns can be identified and reconstructed with very good accuracy even from images where the noise level is ten times stronger than the uncorrupted image.

SIMULATION AND VISUALIZATION OF CNN DYNAMICS

A new simulator for Cellular Neural Networks (CNNs) is presented. In contrast to other simulators, the CNN cells are visualized in a grid structure, the values of input and states being represented by colors. Input and initial images can easily be generated and changed even while the integration of the system is in progress, and an oscilloscope function allows the quantitative study of CNN transients, thus providing insight into the dynamics of the network. For those who are new to the world of CNNs, a series of predefined templates set and demonstrations are available, which makes the simulator a valuable educational tool. Advanced users and CNN expert can examine manually-entered and parametrized templates and carry out experiments in a very broad spectrum of CNN theory and applications, including quantitative behavior, robustness aspects, settling time, state limitations, different output functions and numerical integration methods. The simulator is written in Java and publicly available on WWW and will run on any Web browser of the newer generations.

Time multiplexed color image processing based on a CNN with cell-state outputs

A practical system approach for time-multiplexing cellular neural network (CNN) implementations suitable for processing large and complex images using small CNN arrays is presented. For real size applications, due to hardware limitations, it is impossible to have a one-on-one mapping between the CNN hardware cells and all the pixels in the image involved. This paper presents a practical solution by processing the input image, block by block, with the number of pixels in a block being the same as the number of CNN cells in the array. Furthermore, unlike other implementations in which the output is observed at the hard-limiting block, the very large scale integrated (VLSI) architecture hereby described monitors the outputs from the state node. While previous implementations are mostly suitable for black and white applications because of the thresholded outputs, our approach is especially suitable for applications in color (gray) image processing due to the analog nature of the state node. Experimental complementary metal-oxide-semiconductor (CMOS) chip results in good agreement with theoretical results are presented.

Self-organization in a two-layer CNN

In this work, it is shown that a two-layer cellular neural network (CNN) with constant templates is suitable for generating self-organizing patterns and, therefore, it is able to model complex phenomena. The dynamic behavior of the single two-layer linear CNN cell is studied and the global behavior of the whole CNN is discussed. Different nonlinear phenomena are generated, including autowaves and spirals. Finally, the sensitivity with respect to parametric uncertainties and noise is investigated.

Cellular neural networks to explore complexity

In this paper the fundamentals of Cellular Neural Networks (CNNs) are introduced. Subsequently it is shown that, due to their locally distributed way of exchanging signals, such structures can be used as powerful devices to simulate and to reproduce, in an analog fashion and low cost, complex behaviors, i.e. dynamics commonly encountered in living systems, such as autonomous wave formation and propagation as well as morphogenetical pattern development. In fact it is proven that both of these behaviours can be simulated with CNNs with the same cell structure, and the thoroughly different dynamics can arise only suitably modulating the CNN cell parameters. Therefore a unifying approach to pattern formation and active wave propagation phenomena is presented. The derivation of the complex phenomena is analytically addressed and several simulation results are also reported.

Visualisation of CNN dynamics

A new simulator for cellular neural networks (CNNs) is presented. In contrast to other simulators, the CNN cells are visualised in a grid structure, the values of the input and states being represented by colours. While the integration of the system is in progress, the user can examine the way in which the CNN evolves, thus gaining an insight into its dynamics.

Generation ofn-double scrolls via cellular neural networks

N-double scrolls are chaotic attractors generated by Chua's circuit when its non-linear resistor characteristic is appropriately modified. They have recently been introduced, simulated and studied analytically by Suykens and Vandewalle. In this paper a new approach to generate n-double scroll attractors is introduced. They have been derived from a connection of three simple generalized cellular neural network cells called a state controlled CNN (SC-CNN). In this way it is established that n-double scroll attractors can be generated using an SC-CNN. The circuit implementation of the introduced system and some experimental results referring to the 2-double scroll attractor are reported.

Chua's circuit can be generated by CNN cells

A new realization for the unfolded Chua's circuit is introduced. It has been derived from the connection of three simple generalized cellular neural network (CNN) cells. The main theoretical implication of this result is that the CNN cell represents the primitive for realizing high complex dynamics. The circuit implementation of the introduced system and experimental results referring to the double scroll attractor are reported. >

Methods for image processing and pattern formation in Cellular Neural Networks: a tutorial

In this paper, we demonstrate that many image processing and pattern formation effects of the simple Cellular Neural Network (CNN) can be understood by means of a common approach. By examining the dynamics in the frequency domain, when all CNN cells are in the linear region, the mechanisms for IIR spatial filtering, pattern formation, morphogenesis, and synergetics can be shown to be present, even though each cell has only first-order dynamics. In addition, the method allows many of the standard CNN templates, such as the nonlinear averaging, halftoning, and diffusion templates to be explained in a new light. Through many examples, it is shown how generalizations of these templates can be used to design linear and nonlinear filters for image processing tasks such as low-pass filtering, time-varying spatial filtering, and fingerprint enhancement. >

Chua's oscillator: A compendium of chaotic phenomena

Chua's oscillator is the only real physical object known to date in which chaotic behavior has been observed experimentally and numerically, and proved rigorously. In summarizing the chaotic phenomena observed so far from the oscillator we emphasize its universality by showing how the dynamical phenomena from other 3D oscillators can be reproduced by using Chua's oscillator. The possibility of its use as an elementary cell in cellular neural networks is briefly discussed.

On the applications of the cellular neural network paradigm in mechanical vibrating systems

Cellular neural network (CNNs) are cellular, analog, programmable multidimensional processing arrays with distributed logic and memory. The CNN paradigm is applied to compute the transient response of mechanical vibrating systems. Owing to the fact that here the displacement field has to be computed, the spatially discretized equations of motion are of second order. In this case the standard CNN cell has to be augmented by another capacitance to have second-order cells. The transient response of a mechanical vibrating system with a few thousand degrees of freedom can be computed in real time. >