On the universe of stable cellular neural networks

A cellular neural network (CNN) is a novel analogue circuit architecture with many desirable features. This paper extends previous stability results of CNNs to include classes of strictly sign-symmetric and acyclic templates. We show that most of the 3×3 strictly sign-symmetric templates are stable almost everywhere, with the unknown templates reduced to three classes. We also introduce template graphs and CNN graphs and utilize them to obtain results concerning stability and irreducibility of CNN templates.     

Discrete-time cellular neural networks

A network structure called a discrete-time cellular neural network is introduced. It is derived from cellular neural networks and feedback threshold networks. the architecture is discussed and its advantages are presented. Convergence is proved for a large class of templates and applications are given for the following image-processing tasks: linear thresholding, connected component detection, hole filling, concentric contouring, increasing and decreasing objects step by step, searching for objects with minimal distance, and oscillation.     

Heteroassociative memories via cellular neural networks

In this paper a synthesis procedure for heteroassociative memories using Cellular Neural Networks (CNNs) is presented. The suggested method, by assuring the condition of symmetry of the interconnection matrix, guarantees the complete stability of the designed network, besides providing that all the stored patterns correspond to asymptotically stable equilibrium points. Numerical examples are carried out to show the behaviour of the designed memory with respect to input perturbations. Moreover, the storage capacity and the presence of spurious equilibria have been investigated. © 1998 John Wiley & Sons, Ltd.     

Testability in analogue cellular neural networks

This paper addresses the problem of testing an ACNN by postulating the need for including some extra hardware to render feasible a postfabrication test. the work presented here deals with a test methodology based on adding some extra circuitry to every cell of a regular ACNN. This methodology is just an initial proposal for taking advantage of the network regularity to perform a global test which can be externally interpreted and hence has potential application for reconfiguring the network.     

Stability analysis of generalized cellular neural networks

A rather general class of neural networks, called generalized cellular neural networks (CNNs), is introduced. the new model covers most of the known neural network architectures, including cellular neural networks, Hopfield networks and multilayer perceptrons. Several sets of conditions ensuring the input-output stability and global asymptotic stability of generalized CNNs have been obtained. the conditions for the stability of individual cells are checked in the frequency domain, while the stability of the overall network is analysed in terms of the stability of individual cells and the connectivity characteristics. the results on the global asymptotic stability are useful for the design of a generalized CNN such that the orbit of each state converges to a globally asymptotically stable equilibrium point which depends only on the input and not on the initial state. Such a network defines an algebraic map from the space of external inputs to the space of steady state values of the outputs and hence can accomplish cognitive and computational tasks.     

Estimating optical flow with cellular neural networks

The cellular neural network is a locally interconnected neural network capable of high-speed computation when implemented in analog VLSI. This work describes a CNN algorithm for estimating the optical flow from an image sequence. The algorithm is based on the spatio-temporal filtering approach to image motion analysis and is shown to estimate the optical flow more accurately than a comparable approach proposed previously. Two innovative features of the algorithm are the exploitation of a biological model for hyperacuity and the development of a new class of spatio-temporal filter better suited for image motion analysis than the commonly used space–time Gabor filter. © 1998 John Wiley & Sons, Ltd.     

A study on WTA cellular neural networks

This paper addresses a number of basic issues concerning the dynamics of a class of winner‐take‐all cellular neural networks (WTA CNNs) proposed by Seiler and Nossek. The main result is an analytical estimate for the settling time, which shows from a theoretical point of view that such CNNs are well suited for on‐line applications requiring a large number of units, fast processing speed and a relatively high resolution. Other results are the determination of the largest parameter set that guarantee a correct WTA functionality for all initial conditions and the solution of a conjecture made by Seiler and Nossek. These results are proved by means of a new Lyapunov function to analyse the global dynamical behaviour of the WTA CNNs. Copyright © 2001 John Wiley & Sons, Ltd.     

Frequency domain criteria for cellular neural networks

A dynamical system is called globally asymptotically stable if it has a unique equilibrium point which attracts every trajectory in state space. As a consequence its steady state response is insensitive to initial conditions and then depends only on the input. In this paper some criteria are presented for the global asymptotic stability of cellular neural networks (CNNs), concerning both discrete-time and continuous-time dynamics. The proposed criteria represent necessary and sufficient conditions that can easily be checked by computing the discrete Fourier transform of the template elements. For this reason they have been called frequency domain stability criteria. These criteria provide milder constraints on the template coefficients than required in existing results for general recurrent neural network models. © 1997 by John Wiley & Sons, Ltd.     

Blind signal separation using cellular neural networks

In this paper a two-layer cellular neural network (CNN) is used to separate blind signals. the topological structures of the CNN and the inner parameters are presented. the first CNN layer functions as an adaptive filter which converges asymptotically to an equilibrium point in the mean. A stochastic stability model is used to find conditions under which cells in the first layer converge. Conditions leading to correct equilibrium solutions are also presented using this model. the second CNN layer functions as a signal separator. Simulations show that the CNN blind signal separator has strong robustness and works even better than the theory predicts.     

On the separating capability of cellular neural networks

The cellular neural network is able to perform different image-processing tasks depending on the template values, i.e. the network parameters, used. In the case of linear templates the parameter space is divided into different regions by hyperplanes. Every region is associated with a task, such that all points within that region let the cellular neural network perform the desired task. In this paper a lower and an upper bound for the number of regions that can be separated with binary-input cellular neural networks are given, thus answering the question of how many different-tasks such a cellular neural network can perform.     

Generation of n-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.     

Some dynamic phenomena in delayed cellular neural networks

In this paper we study the dynamic behaviour of delayed cellular neural networks (DCNNs). By means of a rigorous eigenvalue and eigenvector analysis and by numerical simulations we show that simple DCNNs composed of only two cells can exhibit a large variety of dynamic phenomena: stable and unstable closed orbits and chaotic attractors.     

Guiding a mobile robot with cellular neural networks

We show how cellular neural networks (CNNs) are capable of providing the necessary signal processing needed for visual navigation of an autonomous mobile robot. In this way, even complex feature detection and object recognition can be obtained in real time by analogue hardware, making fully autonomous real‐time operation feasible. An autonomous robot was first simulated and then implemented by simulating the CNN with a DSP. The robot is capable of navigating in a maze following lines painted on the floor. Images are processed entirely by a CNN‐based algorithm, and navigation is controlled by a fuzzy‐rule‐based algorithm. Copyright © 2002 John Wiley & Sons, Ltd.     

Absolutely exponential stability in delayed cellular neural networks

In this paper, without assuming the boundedness, monotonicity and differentiability of the activation functions, we present a necessary and sufficient condition ensuring the existence and uniqueness of the equilibrium point of cellular neural network with fixed time delays (DCNNs). Using M‐matrix theory, Liapunov functionals and functions are constructed and employed to establish sufficient conditions for absolutely exponential stability of DCNNs. The results are applicable to DCNNs with both symmetric and non‐symmetric interconnection matrices, and globally Lipschitz continuous activation functions. Copyright © 2002 John Wiley & Sons, Ltd.     

On the dynamic behaviour of two-cell cellular neural networks

A complete study of non-linear differential equations describing two-cell cellular neural networks (CNNs) is presented. the stability properties are investigated and the domains of attraction of the stable fixed points are determined. Also, the conditions for the existence of periodic and homoclinic cycles are stated.     

Nanostructure array of coupled RTDs as cellular neural networks

The processing capabilities of a proposed nanoelectronic device are investigated. The device is considered as a global dynamical system with local circuit model components. The system equations and the corresponding network model are presented. The characteristics of this network model are compared with the cellular neural networks. Certain characteristics of the network are analysed theoretically and demonstrated with circuit‐system level simulations. As a novel property, it is shown that the single layer nanodevice network structure is a basic reaction–diffusion system and it is capable of autowave propagation. Furthermore, the same network structure exhibits several image processing capabilities like image smoothing, edge enhancement, and horizontal or vertical line detection using simple arrangements of the device parameters. Copyright ©2003 John Wiley & Sons, Ltd.     

Detecting moving and standing objects using cellular neural networks

The general framework of motion detection based on discrete time samples of the moving image is defined. Four types of motion detection problem are studied. the simplest one is a model resembling the famous Hubel-Wiesel experiment with a cat's retina for detecting the motion of an object having a given speed in a given direction. the most complicated case is the determination of the vertical and horizontal velocity components of a moving image. Various cloning template sequences are proposed for detecting different types of motion. In the sampled mode the consecutive black-and-white snapshots are fed to the input and to the initial state nodes of the cellular neural network respectively. After the transients have decayed, the output gives the information necessary for detecting the presence or absence of a specific motion as well as for estimating the direction and magnitude of the velocity vector. In continuous mode the sampling process is eliminated by the use of delay-type templates. Conditions are analysed under which the detection is correct. the circuit realization of some motion detectors is discussed and the use of a programmable dual-CNN structure is proposed.     

A rigorous design method for binary cellular neural networks

In order to be able to take full advantage of the great application potential that lies in cellular neural networks (CNNs) we need to have successful design and learning techniques as well. In almost any analogic CNN algorithm that performs an image processing task, binary CNNs play an important role. We observed that all binary CNNs reported in the literature, except for a connected component detector, exhibit monotonic dynamics. In the paper we show that the local stability of a monotonic binary CNN represents sufficient condition for its functionality, i.e. convergence of all initial states to the prescribed global stable equilibria. Based on this finding, we propose a rigorous design method, which results in a set of design constraints in the form of linear inequalities. These are obtained from simple local rules similar to that in elementary cellular automata without having to worry about continuous dynamics of a CNN. In the end we utilize our method to design a new CNN template for detecting holes in a 2D object. © 1998 John Wiley Sons, Ltd.