Farouk Chérif

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.

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.

Stability analysis of delayed Hopfield Neural Networks with impulses via inequality techniques

In this paper, the problem of stability for a class of time-delay Hopfield neural networks with impulsive perturbation is investigated. The existence of a unique equilibrium point is proved by using Arzeli?-Ascoli?s theorem and Rolle?s theorem. Some sufficient stability criteria have proved that the uniform stability, the uniform asymptotic stability, the global asymptotic stability and the global exponential stability of the system, are derived from using the Lyapunov functional method and the linear matrix inequality approach by estimating the upper bound of the derivative of Lyapunov functional. The exponential convergence rate of the equilibrium point is also estimated. Finally, we analyze and interpret some numerical examples showing the efficiency of our theoretical results.

New Results for Impulsive Recurrent Neural Networks with Time-Varying Coefficients and Mixed Delays

In this paper, we shall explain a new result concerning piecewise weighted pseudo almost-periodic solution of impulsive recurrent neural networks with time-varying coefficients and mixed delays. Precisely, some sufficient conditions are given to prove the existence and the exponential stability of piecewise weighted pseudo almost-periodic solution by employing fixed point theorem, generalized Gronwall–Bellman inequality and differential inequality techniques. Finally, an illustrative example is given to demonstrate the effectiveness of our results.

Analysis of Global Asymptotic Stability and Pseudo Almost Periodic Solution of a Class of Chaotic Neural Networks

In this paper we give sufficient conditions ensuring the existence and uniqueness of pseudo almost periodic solution of a class of delayed chaotic neural networks. Further, we study the global asymptotic stability (GAS) of the considered model and give a set of criteria on (GAS) by constructing new Lyapunov functional.

On the dynamics of the high-order type of neural networks with time varying coefficients and mixed delay

This paper discuss the oscillations of high-Order type recurrent delayed neural networks. Various creteria are used to prove the existence and uniqueness of pseudo almost periodic solution in a suitable convex domain. Our method is based on constructing suitable Lyapunov functionals and the well-known Banach contraction mapping principle. Banach fixed point, pseudo almost-periodic functions, high order recurrent neural network.

Dynamics and oscillations of generalized high-order Hopfield neural networks with mixed delays

Abstract Existence and uniqueness of pseudo almost automorphic solutions for a class of high-order Hopfield neural networks are established by employing a suitable fixed point theorem and differential inequality. Moreover, the attractivity and global exponential stability of the pseudo almost automorphic solution are also considered for the system. Two Numerical examples with graphical illustrations are given to illuminate our main results.

Stability and Exponential Synchronization of High-Order Hopfield Neural Networks with Mixed Delays

ABSTRACT This paper investigates the problems of stability and synchronization for high-order recurrent neural networks with mixed delays. Firstly, we establish sufficient conditions to ensure the asymptotic stability and then the exponential synchronization. Furthermore, our results are applied to two chosen systems to demonstrate the effectiveness of the obtained theoretical results.

The Existence and the Stability of Weighted Pseudo Almost Periodic Solution of High-Order Hopfield Neural Network

In this paper, by employing fixed point theorem and differential inequality techniques, some sufficient conditions are given for the existence and the global exponential stability of the unique weighted pseudo almost-periodic solution of high-order Hopfield neural networks with delays. An illustrative example is also given at the end of this paper to show the effectiveness of our results.

Impulsive generalised high-order Recurrent Neural Networks with mixed delays: Stability and periodicity

Abstract In this paper, by employing fixed point theorem, generalized Gronwall–Bellman inequality and differential inequality techniques, some sufficient conditions are given for the existence and the exponential stability of the unique piecewise weighted pseudo almost-periodic solution of impulsive high-order recurrent neural networks with time-varying coefficients and mixed delays. An illustrative example is also given in the end of this paper to show the effectiveness of our results.