Cellular Neural Network Model Research Articles

Novel traveling waves solutions for nonlinear delayed dynamical neural networks with leakage term

In this work, the exponential stability of monotone traveling wave solutions for a class of nonlinear delayed dynamical neural networks with leakage term and distributed delays is investigated. The outcomes of this study are new and has obtained by applying of Ikeharas theorem, the weighted energy method, Taylor formula, comparison principle and the first integral mean value theorem. In addition, the leakage term is considered for the first time in this work to the dynamical model of cellular neural networks.

Displacement Prediction of Surrounding Rock in Tunnel Based on cellular ant algorithm

The deformation of tunnel surrounding rock is the key factor to analyze the stability of surrounding rock. However, due to the influence of many factors and the strong non-linear relationship between the factors, it is difficult to predict the deformation effectively. In this paper, a method based on cellular ant neural network model is proposed to simulate the displacement of surrounding rock with time. The results show that this method is efficient and feasible, and can meet the requirements of engineering and control.

EDGE DETECTION ALGORITHM FOR COLOR IMAGES BASED ON THE REACTION-DIFFUSION EQUATION AND THE CELLULAR NEURAL NETWORK MODEL

EDGE DETECTION ALGORITHM FOR COLOR IMAGES BASED ON THE REACTION-DIFFUSION EQUATION AND THE CELLULAR NEURAL NETWORK MODEL

New Criteria on Stability of Dynamic Memristor Delayed Cellular Neural Networks.

Dynamic memristor (DM)-cellular neural networks (CNNs), which replace a linear resistor with flux-controlled memristor in the architecture of each cell of traditional CNNs, have attracted researchers' attention. Compared with common neural networks, the DM-CNNs have an outstanding merit: when a steady state is reached, all voltages, currents, and power consumption of DM-CNNs disappeared, in the meantime, the memristor can store the computation results by serving as nonvolatile memories. The previous study on stability of DM-CNNs rarely considered time delay, while delay is quite common and highly impacts the stability of the system. Thus, taking the time delay effect into consideration, we extend the original system to DM-D(delay)CNNs model. By using the Lyapunov method and the matrix theory, some new sufficient conditions for the global asymptotic stability and global exponential stability with a known convergence rate of DM-DCNNs are obtained. These criteria generalized some known conclusions and are easily verified. Moreover, we find DM-DCNNs have 3n equilibrium points (EPs) and 2n of them are locally asymptotically stable. These results are obtained via a given constitutive relation of memristor and the appropriate division of state space. Combine with these theoretical results, the applications of DM-DCNNs can be extended to other fields, such as associative memory, and its advantage can be used in a better way. Finally, numerical simulations are offered to illustrate the effectiveness of our theoretical results.

Almost automorphic solutions for Clifford-valued neutral-type fuzzy cellular neural networks with leakage delays on time scales

We propose a class of Clifford-valued neutral-type fuzzy cellular neural network models with leakage delays on time scales, give the definition and basic properties of Clifford-valued almost automorphic functions on time scales, and prove a composition theorem of Clifford-valued almost automorphic functions on time scales, and on this basis, we study the existence and global exponential stability of almost automorphic solutions of this class of neural networks. The research in this paper can unify the research of real-valued neural networks, complex-valued neural networks and quaternion-valued neural networks, as well as the research of continuous-time neural networks and discrete-time neural networks. Finally, an example illustrates the feasibility of the results obtained.

Neural network methodology for real-time modelling of bio-heat transfer during thermo-therapeutic applications.

Real-time simulation of bio-heat transfer can improve surgical feedback in thermo-therapeutic treatment, leading to technical innovations to surgical process and improvements to patient outcomes; however, it is challenging to achieve real-time computational performance by conventional methods. This paper presents a cellular neural network (CNN) methodology for fast and real-time modelling of bio-heat transfer with medical applications in thermo-therapeutic treatment. It formulates nonlinear dynamics of the bio-heat transfer process and spatially discretised bio-heat transfer equation as the nonlinear neural dynamics and local neural connectivity of CNN, respectively. The proposed CNN methodology considers three-dimensional (3-D) volumetric bio-heat transfer behaviour in tissue and applies the concept of control volumes for discretisation of the Pennes bio-heat transfer equation on 3-D irregular grids, leading to novel neural network models embedded with bio-heat transfer mechanism for computation of tissue temperature and associated thermal dose. Simulations and comparative analyses demonstrate that the proposed CNN models can achieve good agreement with the commercial finite element analysis package, ABAQUS/CAE, in numerical accuracy and reduce computation time by 304 and 772.86 times compared to those of with and without ABAQUS parallel execution, far exceeding the computational performance of the commercial finite element codes. The medical application is demonstrated using a high-intensity focused ultrasound (HIFU)-based thermal ablation of hepatic cancer for prediction of tissue temperature and estimation of thermal dose.

Practical Stability with Respect to h-Manifolds for Impulsive Control Functional Differential Equations with Variable Impulsive Perturbations

The present paper is devoted to the problems of practical stability with respect to h-manifolds for impulsive control differential equations with variable impulsive perturbations. We will consider these problems in light of the Lyapunov–Razumikhin method of piecewise continuous functions. The new results are applied to an impulsive control cellular neural network model with variable impulsive perturbations.

A Stochastic Neutral Cellular Neural Networks Model Driven by G-Brownian Motion

In this paper, we propose a new stochastic neutral cellular neural networks model with time delay driven by G -Brownian motion (G-SNCNNs for short). By using fixed point theory and G-expectation analysis methods, the exponential stability and some sufficient conditions on the exponential stability in mean square of the solutions for G-SNCNNs are presented. Finally, a typical case is given to illustrate the effectiveness of the theoretical result.

Analysis of spreading speeds for monotone semiflows with an application to CNNs

The purpose of this work is to investigate the properties of spreading speeds for the monotone semiflows. According to the fundamental work of Liang and Zhao [(2007) Comm. Pure Appl. Math.60, 1–40], the spreading speeds of the monotone semiflows can be derived via the principal eigenvalue of linear operators relating to the semiflows. In this paper, we establish a general method to analyse the sign and the continuity of the spreading speeds. Then we consider a limiting case that admits no spreading phenomenon. The results can be applied to the model of cellular neural networks (CNNs). In this model, we find the rule which determines the propagating phenomenon by parameters.

Neural network modelling of soft tissue deformation for surgical simulation.

This paper presents a new neural network methodology for modelling of soft tissue deformation for surgical simulation. The proposed methodology formulates soft tissue deformation and its dynamics as the neural propagation and dynamics of cellular neural networks for real-time, realistic, and stable simulation of soft tissue deformation. It develops two cellular neural network models; based on the bioelectric propagation of biological tissues and principles of continuum mechanics, one cellular neural network model is developed for propagation and distribution of mechanical load in soft tissues; based on non-rigid mechanics of motion in continuum mechanics, the other cellular neural network model is developed for governing model dynamics of soft tissue deformation. The proposed methodology not only has computational advantage due to the collective and simultaneous activities of neural cells to satisfy the real-time computational requirement of surgical simulation, but also it achieves physical realism of soft tissue deformation according to the bioelectric propagation manner of mechanical load via dynamic neural activities. Furthermore, the proposed methodology also provides stable model dynamics for soft tissue deformation via the nonlinear property of the cellular neural network. Interactive soft tissue deformation with haptic feedback is achieved via a haptic device. Simulations and experimental results show the proposed methodology exhibits the nonlinear force-displacement relationship and associated nonlinear deformation of soft tissues. Furthermore, not only isotropic and homogeneous but also anisotropic and heterogeneous materials can be modelled via a simple modification of electrical conductivity values of mass points.

Stability of traveling wave solutions for nonlinear cellular neural networks with distributed delays

The purpose of this paper is to study the stability of traveling wave solutions for nonlinear cellular neural networks (CNN) with distributed delays. First, we establish two kinds of comparison theorems for the Cauchy problem of the CNN model. With the help of the comparison theorems, we can show that all solutions of the Cauchy problem for the CNN model converge exponentially to the traveling wave solutions when the initial perturbations around the traveling wave solutions belonging to suitable weighted spaces.

Convergence of Neutral Type Fuzzy Cellular Neural Networks with D Operator

A model of neutral type fuzzy cellular neural networks with D operator is proposed. Applying differential inequality techniques, several sufficient conditions are derived to ensure the global exponential convergence of solutions for the proposed neural networks. Finally, a numerical simulation example is given to illustrate the effectiveness of the obtained results.

Global convergence of CNNs with neutral type delays and D operator

A model of cellular neural networks with neutral type delays and D operator is proposed. Applying appropriate differential inequality techniques, several sufficient conditions are derived to ensure...

Pseudo Almost Periodic Shunting Inhibitory Cellular Neural Networks with Multi-proportional Delays

In this paper, a class of shunting inhibitory cellular neural networks model with multi-proportional delays is proposed. Based on the contraction mapping fixed point theorem and differential inequality techniques, some sufficient conditions are obtained for the existence and global exponential stability of pseudo almost periodic solutions for this class of neural networks. In addition, an example and its numerical simulations are given to illustrate our results.

Exponential Stability and Periodic Solutions of Impulsive Neural Network Models with Piecewise Constant Argument

In this paper we introduce an impulsive cellular neural network models with piecewise alternately advanced and retarded argument. The model with the advanced argument is system with strong anticipation. Some sufficient conditions are established for the existence and global exponential stability of a unique periodic solution. The approaches are based on employing Banach’s fixed point theorem and a new integral inequality of Gronwall type with impulses and deviating arguments. The criteria given are easily verifiable, possess many adjustable parameters, and depend on impulses and piecewise constant argument deviations, which provides flexibility for the design and analysis of cellular neural network models. Several numerical examples and simulations are also given to show the feasibility and effectiveness of our results.

Weighted Pseudo Anti‐Periodic Solutions for Cellular Neural Networks with Mixed Delays

AbstractA 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.

Global convergence of CNNs with neutral type delays and D operator

A model of cellular neural networks with neutral type delays and D operator is proposed. Applying appropriate differential inequality techniques, several sufficient conditions are derived to ensure the global exponential convergence of solutions for the proposed neural networks. Finally, a numerical simulation example is given to illustrate the effectiveness of the obtained results.

A Memristive Multilayer Cellular Neural Network With Applications to Image Processing

The memristor has been extensively studied in electrical engineering and biological sciences as a means to compactly implement the synaptic function in neural networks. The cellular neural network (CNN) is one of the most implementable artificial neural network models and capable of massively parallel analog processing. In this paper, a novel memristive multilayer CNN (Mm-CNN) model is presented along with its performance analysis and applications. In this new CNN design, the memristor crossbar circuit acts as the synapse, which realizes one signed synaptic weight with a pair of memristors and performs the synaptic weighting compactly and linearly. Moreover, the complex weighted summation is executed in an efficient way with a proper design of Mm-CNN cell circuits. The proposed Mm-CNN has several merits, such as compactness, nonvolatility, versatility, and programmability of synaptic weights. Its performance in several image processing applications is illustrated through simulations.

Anti-periodic solutions for cellular neural networks with oscillating coefficients in leakage terms

This paper is concerned with the anti-periodic solutions for a class of cellular neural network model with oscillating coefficients in leakage terms. By applying contraction mapping fixed point theorem and differential inequality techniques, we establish some sufficient conditions to guarantee the existence and exponential stability of anti-periodic solutions for this model, which improve and supplement existing ones. Moreover, an example and its numerical simulations are given to support the theoretical results.

Exponential Stability of Pseudo Almost Periodic Solutions for Cellular Neural Networks with Multi-Proportional Delays

This paper concerns with the pseudo almost periodic solutions for a class of cellular neural networks model with multi-proportional delays. By applying contraction mapping fixed point theorem and differential inequality techniques, we establish some sufficient conditions for the existence and exponential stability of pseudo almost periodic solutions for the model, which improve and supplement existing ones. Moreover, an example and its numerical simulation are given to support the theoretical results.