Adnène Arbi

Pseudo-Almost Periodic Solution on Time-Space Scales for a Novel Class of Competitive Neutral-Type Neural Networks with Mixed Time-Varying Delays and Leakage Delays

A competitive neural network model was proposed to describe the dynamics of cortical maps in which, there exist two memories: long-term and short-term. In this paper, we investigate the existence and the exponential stability of the pseudo-almost periodic solution of a system of equations modeling the dynamics of neutral-type competitive neural networks with mixed delays in the time-space scales for the first time. The mixed delays include time-varying delays and continuously distributed ones. Based on contraction principle and the theory of calculus on time-space scales, some new criteria proving the convergence of all solutions of the networks toward the unique pseudo-almost periodic solution are derived by using the ad-hoc Lyapunov–Krasovskii functional. Finally, numerical example with graphical illustration is given to confirm our main results.

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.

Delta-Differentiable Weighted Pseudo-Almost Automorphicity on Time–Space Scales for a Novel Class of High-Order Competitive Neural Networks with WPAA Coefficients and Mixed Delays

In this paper, we consider a novel class of high-order competitive neural networks with mixed delays. Different from the previous literature, we study the existence and exponential stability of weighted pseudo-almost automorphic on time–space scales solutions for the suggested system. Our method is mainly based on the Banach’s fixed point theorem, the theory of calculus on time scales and the Lyapunov–Krasovskii functional method. Moreover, a numerical example is given to show the effectiveness of the main results.

Uniform Asymptotic Stability and Global Asymptotic Stability for Time-Delay Hopfield Neural Networks

In this paper, we consider the uniform asymptotic stability and global asymptotic stability of the equilibrium point for time-delays Hopfield neural networks. Some new criteria of the system are derived by using the Lyapunov functional method and the linear matrix inequality approach for estimating the upper bound of the derivative of Lyapunov functional. Finally, we illustrate a numerical example showing the effectiveness of our theoretical results.