Abdujelil Abdurahman

Finite-time synchronization for memristor-based neural networks with time-varying delays

Memristive network exhibits state-dependent switching behaviors due to the physical properties of memristor, which is an ideal tool to mimic the functionalities of the human brain. In this paper, finite-time synchronization is considered for a class of memristor-based neural networks with time-varying delays. Based on the theory of differential equations with discontinuous right-hand side, several new sufficient conditions ensuring the finite-time synchronization of memristor-based chaotic neural networks are obtained by using analysis technique, finite time stability theorem and adding a suitable feedback controller. Besides, the upper bounds of the settling time of synchronization are estimated. Finally, a numerical example is given to show the effectiveness and feasibility of the obtained results.

Finite-time synchronization for fuzzy cellular neural networks with time-varying delays

In this paper, finite-time synchronization for a class of fuzzy cellular neural networks with time-varying delays is investigated based on the finite-time stability theory. By applying the inequality technique and the analysis method, some new and useful criteria of finite-time synchronization for the addressed network are derived in terms of p-norm. Finally, two examples with their numerical simulations are given to show the feasibility and effectiveness of the developed synchronization method.

Exponential lag synchronization for memristor-based neural networks with mixed time delays via hybrid switching control

Abstract In this paper, the exponential lag synchronization for a class of memristor-based neural networks with mixed time-delays is investigated via hybrid switching control method. Based on the theory of differential equations with discontinuous right-hand side, several new sufficient conditions ensuring the exponential lag synchronization of memristor-based chaotic neural networks are obtained by designing two diffident hybrid switching controllers and constructing novel Lyapunov functionals. Finally, a numerical example with simulation is given to show the effectiveness and feasibility of the obtained results.

The existence and stability of the anti-periodic solution for delayed Cohen-Grossberg neural networks with impulsive effects

In this paper, we investigate the existence and global exponential stability of the anti-periodic solution for delayed Cohen-Grossberg neural networks with impulsive effects. First, based on the Lyapunov functional theory and by applying inequality technique, we give some new and useful sufficient conditions to ensure existence and exponential stability of the anti-periodic solutions. Then, we present an example with numerical simulations to illustrate our results.

New results on exponential synchronization of memristor-based neural networks with discontinuous neuron activations

This paper investigates the exponential synchronization of delayed memristor-based neural networks (MNNs) with discontinuous activation functions. Based on the framework of Filippov solution and differential inclusion theory, using new analytical techniques and introducing suitable Lyapunov functionals, some novel sufficient conditions ensuring the exponential synchronization of considered networks are established via two types of discontinuous controls: linear feedback control and adaptive control. In particular, we extend the discontinuous control strategies for neural networks with continuous dynamics to MNNs with discontinuous activations. Numerical simulations are given to show the effectiveness of the theoretical results. Our approach and theoretical results have a leading significance in the design of synchronized MNN circuits involving discontinuous activations and time-varying delays.

Function projective synchronization of memristor-based Cohen-Grossberg neural networks with time-varying delays.

AbstractThis paper deals with the problem of function projective synchronization for a class of memristor-based Cohen–Grossberg neural networks with time-varying delays. Based on the theory of differential equations with discontinuous right-hand side, some novel criteria are obtained to realize the function projective synchronization of addressed networks by combining open loop control and linear feedback control. As some special cases, several control strategies are given to ensure the realization of complete synchronization, anti-synchronization and the stabilization of the considered memristor-based Cohen–Grossberg neural network. Finally, a numerical example and its simulations are provided to demonstrate the effectiveness of the obtained results.

Lag synchronization for Cohen–Grossberg neural networks with mixed time-delays via periodically intermittent control

ABSTRACT In this paper, the exponential lag synchronization for a class of Cohen–Grossberg neural networks with discrete time-delays and distributed delays is investigated via periodically intermittent control. Some simple and useful criteria are derived by using mathematical induction method and the analysis technique which are different from the methods employed in correspondingly previous works. Finally, two examples and their numerical simulations are given to demonstrate the effectiveness of the proposed control schemes.

Global generalized exponential stability for a class of nonautonomous cellular neural networks via generalized Halanay inequalities

Abstract This paper investigates a new type of stability, namely global generalized exponential stability of the nonautonomous delayed cellular neural networks. Several novel delay-dependent sufficient conditions are established by applying a new generalized Halanay inequality. In these conditions, the boundedness of time-varying delays and coefficients are not required. In addition, the effectiveness of these conditions is illustrated by two numerical examples.

Parameter identification based on finite-time synchronization for Cohen–Grossberg neural networks with time-varying delays

In this paper, the finite-time synchronization problem for chaotic Cohen–Grossberg neural networks with unknown parameters and time-varying delays is investigated by using finite-time stability theory. Firstly, based on the parameter identification of uncertain delayed neural networks, a simple and effective feedback control scheme is proposed to tackle the unknown parameters of the addressed network. Secondly, by modifying the error dynamical system and using some inequality techniques, some novel and useful criteria for the finite-time synchronization of such a system are obtained. Finally, an example with numerical simulations is given to show the feasibility and effectiveness of the developed methods.

Global asymptotic and robust stability of inertial neural networks with proportional delays

Abstract This paper is concerned with the global asymptotic stability and global robust stability of inertial neural networks with proportional delays. First, by using linear matrix inequality and constructing appropriate Lyapunov functional, several sufficient conditions are obtained for the global asymptotic stability of inertial neural networks with proportional delays. Furthermore, the problem of global robust stability of the network under the assumptions that the network parameters are uncertain and bounded is studied. Finally, some simulation examples are presented to demonstrate the effectiveness of the proposed method.