Abdullah Al-Mazrooei

Synchronization of Switched Interval Networks and Applications to Chaotic Neural Networks

This paper investigates synchronization problem of switched delay networks with interval parameters uncertainty, based on the theories of the switched systems and drive-response technique, a mathematical model of the switched interval drive-response error system is established. Without constructing Lyapunov-Krasovskii functions, introducing matrix measure method for the first time to switched time-varying delay networks, combining Halanay inequality technique, synchronization criteria are derived for switched interval networks under the arbitrary switching rule, which are easy to verify in practice. Moreover, as an application, the proposed scheme is then applied to chaotic neural networks. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.

Finite-time boundedness and stabilization of uncertain switched neural networks with time-varying delay

This paper deals with the finite-time boundedness and stabilization problem for a class of switched neural networks with time-varying delay and parametric uncertainties. Based on Lyapunov-like function method and average dwell time technique, some sufficient conditions are derived to guarantee the finite-time boundedness of considered uncertain switched neural networks. Furthermore, the state feedback controller is designed to solve the finite-time stabilization problem. Moreover, the proposed sufficient conditions can be simplified into the form of linear matrix equalities for conveniently using Matlab LMI toolbox. Finally, two numerical examples are given to show the effectiveness of the main results.

Pinning synchronization of coupled inertial delayed neural networks

Abstract The paper is devoted to the investigation of synchronization for an array of linearly and diffusively coupled inertial delayed neural networks (DNNs). By placing feedback control on a small fraction of network nodes, the entire coupled DNNs can be synchronized to a common objective trajectory asymptotically. Two different analysis methods, including matrix measure strategy and Lyapunov–Krasovskii function approach, are employed to provide sufficient criteria for the synchronization control problem. Comparisons of these two techniques are given at the end of the paper. Finally, an illustrative example is provided to show the effectiveness of the obtained theoretical results.

Delay-Dependent Stability Criterion of Caputo Fractional Neural Networks with Distributed Delay

This paper is concerned with the finite-time stability of Caputo fractional neural networks with distributed delay. The factors of such systems including Caputo’s fractional derivative and distributed delay are taken into account synchronously. For the Caputo fractional neural network model, a finite-time stability criterion is established by using the theory of fractional calculus and generalized Gronwall-Bellman inequality approach. Both the proposed criterion and an illustrative example show that the stability performance of Caputo fractional distributed delay neural networks is dependent on the time delay and the order of Caputo’s fractional derivative over a finite time.

Applications of Laplacian spectra for n-prism networks

In this paper, the properties of the Laplacian matrices for the n-prism networks are investigated. We calculate the Laplacian spectra of n-prism graphs which are both planar and polyhedral. In particular, we derive the analytical expressions for the product and the sum of the reciprocals of all nonzero Laplacian eigenvalues. Moreover, these results are used to handle various problems that often arise in the study of networks including Kirchhoff index, global mean-first passage time, average path length and the number of spanning trees. These consequences improve and extend the earlier results. HighlightsWe propose the structure of n-prism networks.We calculate the Laplacian spectra of n-prism networks.We deduce expressions for product and sum of reciprocals of all nonzero Laplacian-eigenvalues.Kirchhoff index, GMFPT, average path length and the number of spanning trees are obtained.

Solving Generalized Mixed Equilibria, Variational Inequalities, and Constrained Convex Minimization

We propose implicit and explicit iterative algorithms for finding a common element of the set of solutions of the minimization problem for a convex and continuously Frechet differentiable functional, the set of solutions of a finite family of generalized mixed equilibrium problems, and the set of solutions of a finite family of variational inequalities for inverse strong monotone mappings in a real Hilbert space. We prove that the sequences generated by the proposed algorithms converge strongly to a common element of three sets, which is the unique solution of a variational inequality defined over the intersection of three sets under very mild conditions.

Hybrid viscosity approximation methods for general systems of variational inequalities in Banach spaces

Let X be a uniformly convex and 2-uniformly smooth Banach space. In this paper, we propose an implicit iterative method and an explicit iterative method for solving a general system of variational inequalities (in short, GSVI) in X based on Korpelevich’s extragradient method and viscosity approximation method. We show that the proposed algorithms converge strongly to some solutions of the GSVI under consideration. When X is a 2-uniformly smooth Banach space with weakly sequentially continuous duality mapping, we also propose two methods, which were inspired and motivated by Korpelevich’s extragradient method and Mann’s iterative method. Furthermore, it is also proven that the proposed algorithms converge strongly to some solutions of the considered GSVI.MSC:49J30, 47H09, 47J20.

Synchronization of the Coupled Distributed Parameter System with Time Delay via Proportional-Spatial Derivative Control

By combining parabolic partial differential equation (PDE) theory with Lyapunov technique, the synchronization is studied for a class of coupled distributed parameter systems (DPS) described by PDEs. First, based on Kronecker product and Lyapunov functional, some easy-to-test sufficient condition is given to ensure the synchronization of coupled DPS with time delay. Secondly, in the case that the whole coupled system cannot synchronize by itself, the proportional-spatial derivative (P-sD) state feedback controller is designed and applied to force the network to synchronize. The sufficient condition on the existence of synchronization controller is given in terms of a set of linear matrix inequalities. Finally, the effectiveness of the proposed control design methodology is demonstrated in numerical simulations.

Power-rate synchronization of coupled genetic oscillators with unbounded time-varying delay.

In this paper, a new synchronization problem for the collective dynamics among genetic oscillators with unbounded time-varying delay is investigated. The dynamical system under consideration consists of an array of linearly coupled identical genetic oscillators with each oscillators having unbounded time-delays. A new concept called power-rate synchronization, which is different from both the asymptotical synchronization and the exponential synchronization, is put forward to facilitate handling the unbounded time-varying delays. By using a combination of the Lyapunov functional method, matrix inequality techniques and properties of Kronecker product, we derive several sufficient conditions that ensure the coupled genetic oscillators to be power-rate synchronized. The criteria obtained in this paper are in the form of matrix inequalities. Illustrative example is presented to show the effectiveness of the obtained results.

Hybrid iterative method for systems of generalized equilibria with constraints of variational inclusion and fixed point problems

AbstractIn this paper, we introduce and analyze an iterative algorithm by the hybrid iterative method for finding a solution of the system of generalized equilibrium problems with constraints of several problems: a generalized mixed equilibrium problem, finitely many variational inclusions, and the common fixed point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense and infinitely many nonexpansive mappings in a real Hilbert space. Weak convergence result under mild assumptions will be established. MSC: 49J30, 47H09, 47J20, 49M05.