Convergence of asymptotic systems of non-autonomous neural network models with infinite distributed delays

In this paper we investigate the global convergence of solutions of non-autonomous Hopfield neural network models with discrete time-varying delays, infinite distributed delays, and possible unbounded coefficient functions. Instead of using Lyapunov functionals, we explore intrinsic features between the non-autonomous systems and their asymptotic systems to ensure the boundedness and global convergence of the solutions of the studied models. Our results are new and complement known results in the literature. The theoretical analysis is illustrated with some examples and numerical simulations.The paper was supported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the "Fundacao para a Ciencia e a Tecnologia", through the Project PEstOE/MAT/UI0013/2014. The author thanks the referee for valuable comments.info:eu-repo/semantics/publishedVersio

Existence and stability of a periodic solution of a general difference equation with applications to neural networks with a delay in the leakage terms

In this paper, a new global exponential stability criterion is obtained for a general multidimensional delay difference equation using induction arguments. In the cases that the difference equation is periodic, we prove the existence of a periodic solution by constructing a type of Poincar\'e map. The results are used to obtain stability criteria for a general discrete-time neural network model with a delay in the leakage terms. As particular cases, we obtain new stability criteria for neural network models recently studied in the literature, in particular for low-order and high-order Hopfield and Bidirectional Associative Memory(BAM).Comment: 20 pages, 3 figure

Delay-Dependent Dynamics of Switched Cohen-Grossberg Neural Networks with Mixed Delays

This paper aims at studying the problem of the dynamics of switched Cohen-Grossberg neural networks with mixed delays by using Lyapunov functional method, average dwell time (ADT) method, and linear matrix inequalities (LMIs) technique. Some conditions on the uniformly ultimate boundedness, the existence of an attractors, the globally exponential stability of the switched Cohen-Grossberg neural networks are developed. Our results extend and complement some earlier publications

Differenciál- és differenciaegyenletek kvalitatív és kvantitatív elmélete alkalmazásokkal = Qualitative and quantitative theory of differential and difference equations with applications

Kutatásaink a következő témakörökhöz kapcsolódtak: Megoldások aszimptotikus jellemzése és stabilitása; integrálegyenletek és egyenlőtlenségek mértékterekben; differenciálegyenletek megoldásainak paraméterektől való differenciálható függése, paraméterek becslése; állapotfüggő késleltetésű differenciálegyenletek stabilitása. A 2004-2007 kutatási időszakban 31 publikációnk jelent meg. Dolgoztainkra az elmúlt négy évben 575, ezen belül a kutatási periódusban megjelent 31 publikációnkra pedig 57 hivatkozást regisztráltunk. Eredményeinkről 9 plenáris, 33 meghívott szekció és 16 szekció előadásban számoltunk be nemzetközi konferenciákon. Ezeken kívül 34 meghívott előadást tartottunk különböző hazai és külföldi egyetemek szakmai szemináriumain. | Our research is related to the following topics: Asymptotic characterization and stability of solutions; integral equations and inequalities in measure spaces; differentiability of the solutions with respect to the parameters, and parameter estimation methods; stability of differential equations with state-dependent delays. 31 of our pubications have appeared in the research period 2004-2007. We have counted 575 citations of our papers in the last four years, including 57 citations of our 31 papers published in this period. We gave 9 plenary, 33 invited, and 16 contributed talks at international conferences, and 34 invited talks at research seminars of national and foreign universities