Complex behavior of polynomial FitzHugh–Nagumo cellular neural network model

We describe a novel cellular connectionist neural network model for the implementation of clustering-based Bayesian image segmentation with Gibbs random-field spatial constraints. The success of this algorithm is largely due to the neighborhood constraints modeled by the Gibbs random field. However, the iterative enforcement of the neighborhood constraints involved in the Bayesian estimation would generally require tremendous computational power. Such computational requirement hinders the real-time application of the Bayesian image segmentation algorithms. The cellular connectionist model proposed aims at implementing the Bayesian image segmentation with real-time processing potentials. With a cellular neural network architecture mapped onto the image spatial domain, the powerful Gibbs spatial constraints are realized through the interactions among neurons connected through their spatial cellular layout. This network model is structurally similar to the conventional cellular network. However, in this new cellular model, the processing elements designed within the connectionist network are functionally more versatile to meet the challenging needs of Bayesian image segmentation based on the Gibbs random field. We prove that this cellular neural network does converge to the desired steady state with a properly designed update scheme. Examples of CT volumetric medical image segmentation are presented to demonstrate the potential of this cellular neural network for a specific image segmentation application.

The paper considers the full-range (FR) model of cellular neural networks (CNNs) with ideal hard-limiter non-linearities that limit the allowable range of the neuron state variables. It is also supposed that there is a concentrated delay (D) in the neuron interconnections. Due to the presence of multivalued nonlinearities the D-FRCNN model is mathematically described by a retarded differential inclusion. The main result is a rigorous proof that, in the case of nonsymmetric cooperative (nonnegative) interconnections, and delayed interconnections, the semiflow generated by D-FRCNNs is monotone, and that monotonicity implies some basic restrictions on the long-term behavior of the solutions. The result is compared with recent results in the literature on semiflows generated by cooperative standard CNNs, with and without delays.

In this paper we show cellular neural network (CNN) models of some basic types of cells characterized by diverse spiking patterns. After presenting some preliminary models (ion channels, neurons), CNN models of action potential generation are given, followed by an analysis of the rate-coding capabilities of the models. Furthermore, we show CNN models of synaptic connections. Finally, CNN models of neurons with diverse intrinsic firing patterns are presented.

A model of cellular neural networks with mixed delays is proposed. Applying contraction mapping fixed point theorem and differential inequality technique, several sufficient conditions are derived to ensure the existence and exponential stability of weighted pseudo anti‐periodic solutions for the proposed neural networks. Finally, a numerical simulation example is given to illustrate the effectiveness of the obtained results.

In the present work an adaptation of the cellular neural network (CNN) model to grey scale image processing is proposed. This task is performed programming the network to work as a classical spatial filter, taking advantage of the neural network structure in order to improve the filtering effects. This enhancement is carried out by the inclusion of the feedback of the state variables and the adaptation of the input bias of every neuron based on the brightness of the image. A proper choice of the gain of the output function may also improve some of the network capabilities.

CNNEDGEPOT: CNN based edge detection of 2D near surface potential field data

Application of cellular neural network (CNN) to the prediction of missing air pollutant data

The mathematical model of a cellular neural network (CNN) consists of a large set of coupled non‐linear differential equations that has been mainly studied through numerical simulations; the knowledge of the dynamic behaviour is essential for developing rigorous design methods and for establishing new applications. This manuscript is devoted to a comparison of the dynamic behaviours of two CNN models: the original Chua–Yang model and the full‐range model that was exploited for VLSI implementations. It is shown that, even if the two models exhibit similar properties, they are not topologically equivalent, i.e. there exist sets of identical parameters for which they present a qualitatively different dynamic behaviour. Copyright © 2003 John Wiley & Sons, Ltd.

Theoretic design of differential minimax controllers for stochastic cellular neural networks

In this paper, a new phenomenon observed in cellular neural networks (CNNs) is treated. Some experimental results will be introduced, showing that spatio-temporal noise in two layers-two dimensional CNN architectures could improve the propagation of damped traveling waves. The CNN model and templates are reported and computer simulation results will emphasize the innovative results.

The sigma-delta cellular neural network (SD-CNN) is a complete framework of a spatial domain sigma-delta modulator, and has a very high image reconstruction (AD-to-DA) performance. In this architecture, the A-template, given by a 2D low pass filter (LPF), is used for a digital to analogue converter (DAC), the C-template works as an integrator, and the nonlinear output function is for the bilevel output. By exploiting to the nonlinear optimization ability of CNN spatio-temporal dynamics, optimal binary and reconstruction image can be obtained. However, in the conventional SD-CNN, the Gaussian LPF, whose coefficients are real number, is used as the A-template. This filter coefficients requirement is one of major factors that restricts a hardware implementation. In this paper, a SD-CNN having hardware-friendly filter coefficients is proposed. Moreover its AD and DA performance is confirmed by some experiments.

An accelerated-time simulation of car traffic on a motorway using a CAS

An optoelectronic model of discrete time cellular neural networks (DTCNN) is presented. Connections between cells and parallel input-output are realized using optoelectronic devices. As an emitter-receiver device an optical thyristor is applied. Connections between cells are realized by diffractive Damman gratings. We propose a dual rail system for early processing of binary images. The CNN system performs mathematical morphology and space logic operations.

Understanding urban expansion patterns is critical for sustainable land-use planning, particularly in rapidly developing regions. This study employs an integrated geographic ınformation system-based approach utilizing the MOLUSCE plugin in QGIS to predict future Land Use and Land Cover (LULC) changes in Sakarya Province, Türkiye, from 2011 to 2040. While cellular automata-artificial neural network and Markov Chain models have been extensively utilized in LULC research, their application to mid-sized Turkish provinces remains insufficiently explored. This study addresses that gap by providing the first comprehensive spatiotemporal analysis of Sakarya’s urban growth trends, incorporating environmental impact assessments alongside predictive modeling. The results indicate a 3.43% decline in agricultural areas and a 0.43% decrease in forests from 2011 to 2024, with continued urban expansion projected through 2040. These findings underscore the urgent need for sustainable zoning policies and conservation strategies to mitigate the adverse effects of urbanization on natural resources. The study not only enhances regional LULC modeling efforts but also provides a scalable framework for other developing urban centers facing similar land-use challenges.

This paper describes procedures to build custom‐tailored behavioural models of cellular neural networks (CNNs), and acompanion tool to run these models. The main property of the CNNs is the emerging behaviour, i.e. new phenomena arise from the interactions of thousands of identical cells. The existence of these phenomena need is to be checked during the design phase, which requires a full network simulation and therefore constitutes a very time‐consuming step of circuit verification. To solve this task as a modelling problem, we introduce a new behavioural model optimization technique. Starting from a user‐defined set of block models, the proposed framework produces an optimized selection which is used to build up a full‐chip model. The optimization goal is the minimization of the simulation CPU time and the maximization of the time domain precision. A dedicated environment has been developed for efficient numerical simulation; this environment is briefly described in the paper. Two case studies are also presented to demonstrate the effectivity of the technique. Copyright © 2002 John Wiley & Sons, Ltd.