Chaouki Aouiti

Pseudo Almost Automorphic Solutions of Recurrent Neural Networks with Time-Varying Coefficients and Mixed Delays

In this paper, existence, uniqueness and global exponential stability of pseudo almost automorphic solutions for a class of recurrent neural networks with time-varying coefficients and mixed delays are established by employing the fixed point theorem and differential inequality. Numerical example with graphical illustration is given to illuminate our main results.

Piecewise Pseudo Almost Periodic Solution for Impulsive Generalised High-Order Hopfield Neural Networks with Leakage Delays

Existence of piecewise differentiable pseudo almost-periodic solutions for a class of impulsive high-order Hopfield neural networks with leakage delays are established by employing the fixed point theorem, differential inequality and Lyapunov functionals. The results of this paper are new and they supplement previously known works. Numerical example with graphical illustration is given to illuminate our main results.

Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays

In this article, we consider a class of neutral impulsive shunting inhibitory cellular neural networks with time varying coefficients and leakage delays. We study the existence and the exponential stability of the piecewise differentiable pseudo almost-periodic solutions and establish sufficient conditions for the existence and exponential stability of such solutions. An example is provided to illustrate the theory developed in this work.

The design of beta basis function neural network and beta fuzzy systems by a hierarchical genetic algorithm

We propose an evolutionary method for the design of beta basis function neural networks (BBFNN) and of beta fuzzy systems (BFS). Classical training algorithms start with a predetermined network structure for neural networks and with a predetermined number of fuzzy rules for fuzzy systems. Generally speaking both the neural network and the fuzzy systems are either insufficient or overcomplicated. This paper describes a hierarchical genetic learning model of the BBFNN and the BFS. In order to examine the performance of the proposed algorithm, it is used for functional approximation problem for the case of BBFNN and for the identification of an induction machine fuzzy plant model for the case of BFS. The results obtained have been encouraging.

Oscillation of impulsive neutral delay generalized high-order Hopfield neural networks

Abstract In this paper, the existence and the exponential stability of piecewise differentiable pseudo-almost periodic solutions for a class of impulsive neutral high-order Hopfield neural networks with mixed time-varying delays and leakage delays are established by employing the fixed point theorem, Lyapunov functional method and differential inequality. Numerical example with graphical illustration is given to illuminate our main results.

A hierarchical genetic algorithm for the design of beta basis function neural network

We propose an evolutionary neural network-training algorithm for beta basis function neural networks (BBFNN). Classic training algorithms for neural networks start with a predetermined network structure. Generally the network resulting from learning applied to a predetermined architecture is either insufficient or over-complicated. This paper describes a hierarchical genetic learning model of the BBFNN. In order to examine the performance of the proposed algorithm, they were used for the approximation problems. The results obtained are very satisfactory with respect to the relative error.

Stability analysis for delayed high-order type of Hopfield neural networks with impulses

This paper can be regarded as the continuation of the work of the authors contained in papers (2015). At the same time, it represents the extension of the papers Lou and Cui (2007, 24]), Sannay (2007, 34]) and Acka et al. (2004, 1]). This work discusses a generalized model of high-order Hopfield-type neural networks with time-varying delays. By utilizing Lyapunov functional method and the linear inequality approach, some new stability criteria for such system are derived. The results are related to the size of delays and impulses. The exponential convergence rate of the equilibrium point is also estimated. Finally, we analyze and interpret four numerical examples proving the efficiency of our theoretical results and showing that impulse can be used to stabilize and exponentially stabilize some high-order Hopfield-type neural networks. HighlightsThis manuscript represents the continuation of the previous work of the authors, related to a class of delayed high-order type of Hopfield neural networks with Impulses.Some delay-dependent criteria for various stability types of a generalized model of high-order Hopfield-type neural networks with time-varying delays are derived. The results are related to the size of delays and impulses;The delay-independent uniform stability criteria for a generalized model of high-order Hopfield-type neural networks with time-varying delays are derived;The exponential convergence rate of the equilibrium point is estimated;The operator of impulse is used to stabilize and exponentially stabilize some high-order Hopfield-type neural networks.

Weighted pseudo almost-periodic solutions of shunting inhibitory cellular neural networks with mixed delays

Abstract In this paper, we prove the existence and the global exponential stability of the unique weighted pseudo almost-periodic solution of shunting inhibitory cellular neural networks with mixed time-varying delays comprising different discrete and distributed time delays. Some sufficient conditions are given for the existence and the global exponential stability of the weighted pseudo almost-periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper complement the previously known ones. Finally, an illustrative example is given to demonstrate the effectiveness of our results.

Finite time boundedness of neutral high-order Hopfield neural networks with time delay in the leakage term and mixed time delays

Abstract This article deals with the finite time boundedness (FTB) and FTB-stabilization problem for a general class of neutral high-order Hopfield neural networks (NHOHNNs) with time delay in the leakage term and mixed time delays. The mixed time delays consist of both discrete time-varying delays and infinite distributed delays. By using the topological degree theory, sufficient conditions are established to prove the existence of equilibrium points. Then, the Lyapunov–Krasovskii functional (LKF) method is used to prove sufficient conditions for the FTB. These conditions are in the form of linear matrix inequalities (LMIs) and can be numerically checked. Furthermore, a state feedback control is constructed to solve the FTB-stabilization problem. Finally, some numerical examples are presented to show the effectiveness of our main results.

Dynamics of new class of hopfield neural networks with time-varying and distributed delays

Abstract In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution, which is also its derivative pseudo almost periodic. This results are without resorting to the theory of exponential dichotomy. Furthermore, by employing the suitable Lyapunov function, some delay-independent sufficient conditions are derived for exponential convergence. The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity. Lastly, two examples are given to demonstrate the validity of the proposed theoretical results.