Closed-form periodic solutions for piecewise-linear vibrating systems

In this paper, the global robust point dissipativity of an uncertain neural networks model with mixed time-varying delays is investigated, based on Lyapunov theory and inequality techniques. First, the concept of global robust point dissipativity is introduced. Next, some sufficient conditions are given for checking the global robust point dissipativity and the global exponential robust dissipativity of the uncertain neural networks model. Finally, illustrated examples are given to show the effectiveness of our results.     

Dissipativity analysis of stochastic neural networks with time delays

This paper is concerned with the dissipativity problem of stochastic neural networks with time delay. A new stochastic integral inequality is first proposed. By utilizing the delay partitioning technique combined with the stochastic integral inequalities, some sufficient conditions ensuring mean-square exponential stability and dissipativity are derived. Some special cases are also considered. All the given results in this paper are not only dependent upon the time delay, but also upon the number of delay partitions. Finally, some numerical examples are provided to illustrate the effectiveness and improvement of the proposed criteria.     

Robust dissipativity analysis of neural networks with time-varying delay and randomly occurring uncertainties

This paper investigates the problem of robust dissipativity analysis for uncertain neural networks with time-varying delay. The norm-bounded uncertainties enter into the neural networks in randomly ways, and such randomly occurring uncertainties (ROUs) obey certain mutually uncorrelated Bernoulli distributed white noise sequences. By employing the linear matrix inequality (LMI) approach, a sufficient condition is established to ensure the robust stochastic stability and dissipativity of the considered neural networks. Some special cases are also considered. Two numerical examples are given to demonstrate the validness and the less conservatism of the obtained results.     

Dynamic stability recognition of cylindrical shallow shells in Kelvin–Voigt viscoelastic medium under transverse white noise excitation

Nonlinear Dynamics - This paper investigates the problem of delay-dependent dissipativity for a class of Markovian jump neural networks with a time-varying delay. A generalized integral inequality...     

Non-fragile extended dissipative state estimation for delayed discrete-time neural networks: application to quadruple tank process model

Nonlinear Dynamics - This paper deals with the non-fragile state estimator design to study the robust extended dissipativity criterion for a class of discrete-time neural networks (DNNs) involving...     

On improved passivity criteria of uncertain neural networks with time-varying delays

In this paper, the problem of passivity analysis for uncertain neural networks with time-varying delays is considered. By constructing an augmented Lyapunov–Krasovskii’s functional and some novel analysis techniques, improved delay-dependent criteria for checking the passivity of the neural networks are established. The proposed criteria are represented in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical examples are included to show the superiority of our results.     

Global Attractivity and Global Exponential Stability for Delayed Hopfield Neural Network Models

ＩｎｔｒｏｄｕｃｔｉｏｎＨｏｐｆｉｅｌｄｎｅｕｒａｌｎｅｔｗｏｒｋｍｏｄｅｌｉｓｏｎｅｏｆｔｈｅｍｏｓｔｐｏｐｕｌａｒｍｏｄｅｌｓｉｎｔｈｅｌｉｔｅｒｒａｔｕｒｅｏｆａｒｔｉｆｉｃｉａｌｎｅｕｒａｌｎｅｔｗｏｒｋｓ,ｗｈｉｃｈｉｓｄｅｓｃｒｉｂｅｄｂｙｔｈｅｆｏｌｌｏｗｉｎｇｎｏｎｌｉｎｅａｒｄｙｎａｍｉｃｓｅｑｕａｔｉｏｎｓ[1,2 ]:Ｃｉｄｕｉ(ｔ)ｄｔ =-ｕｉ(ｔ)Ｒｉ ∑ｎｊ=1Ｔｉｊｇｊ(ｕｊ(ｔ) ) Ｉｉ　　 (ｉ=1 ,2 ,… ,ｎ) ,( 1 )ｗｈｅｒｅｎ≥ 2ｉｓｔｈｅｎｕｍｂｅｒｏｆｎｅｕｒｏｎｓｉｎｔｈｅ…     

Passivity of uncertain neural networks with both leakage delay and time-varying delay

In this paper, the passivity problem is investigated for a class of uncertain neural networks with leakage delay and time-varying delay as well as generalized activation functions. By constructing appropriate Lyapunov–Krasovskii functionals, and employing Newton–Leibniz formulation and the free-weighting matrix method, several delay-dependent criteria for checking the passivity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Two examples with simulations are given to show the effectiveness and less conservatism of the proposed criteria.     

Exponential synchronization of chaotic neural networks: a matrix measure approach

Based on matrix measure and Halanay inequality, exponential synchronization of a class of chaotic neural networks with time-varying delays is investigated. Without constructing Lyapunov function, some simple but generic criteria for exponential synchronization of chaotic neural networks are derived. It is shown that the obtained results are easy to verify and simple to implement in practice. Two examples are given to illustrate the effectiveness of the presented synchronization scheme.     

Exponential stability in the mean square for stochastic neural networks with mixed time-delays and Markovian jumping parameters

In this paper, the stability analysis problem is considered for a class of stochastic neural networks with mixed time-delays and Markovian jumping parameters. The mixed delays include discrete and distributed time-delays, and the jumping parameters are generated from a continuous-time discrete-state homogeneous Markov process. The aim of this paper is to establish some criteria under which the delayed stochastic neural networks are exponentially stable in the mean square. By constructing suitable Lyapunov functionals, several stability conditions are derived on the basis of inequality techniques and the stochastic analysis. An example is also provided in the end of this paper to demonstrate the usefulness of the proposed criteria.     

Passivity analysis of uncertain neural networks with mixed time-varying delays

This paper addresses the passivity problem for uncertain neural networks with both discrete and distributed time-varying delays. It is assumed that the parameter uncertainties are norm-bounded. By construction of an augmented Lyapunov–Krasovskii functional and utilization of zero equalities, improved passivity criteria for the networks are derived in terms of linear matrix inequalities (LMIs) via new approaches. Through three numerical examples, the effectiveness to enhance the feasible region of the proposed criteria is demonstrated.     

Function projective synchronization of impulsive neural networks with mixed time-varying delays

In this paper, the exponential function projective synchronization of impulsive neural networks with mixed time-varying delays is investigated. Based on the contradiction method and analysis technique, some novel criteria are obtained to guarantee the function projective synchronization of considered networks via 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 addressed neural networks. Finally, two examples and their numerical simulations are given to show the effectiveness and feasibility of the proposed synchronization schemes.     

New augmented Lyapunov–Krasovskii functional approach to stability analysis of neural networks with time-varying delays

This paper is concerned with the problem of stability analysis for neural networks with time-varying delays. By constructing a newly augmented Lyapunov functional and some novel techniques, delay-dependent criteria to guarantee the asymptotic stability of the concerned networks are derived in terms of linear matrix inequalities (LMIs). The improvement of feasible region of the proposed criteria comparing with the previous works is shown by two numerical examples.     

Projective synchronization of neural networks with mixed time-varying delays and parameter mismatch

In this paper, the projective synchronization of neural networks with mixed time-varying delays and parameter mismatch is discussed. Due to parameter mismatch and projective factor, complete projective synchronization cannot be achieved. Therefore, a new weak projective synchronization scheme is proposed to ensure that coupled neural networks are in a state of synchronization with an error level. Several criteria are derived and the error level is estimated by applying a generalized Halanay inequality and matrix measure. Finally, a numerical example is given to verify the efficiencies of theoretical results.     

Delay-independent exponential stability of stochastic Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms

Different from the approaches used in the earlier papers, in this paper, the Halanay inequality technique, in combination with the Lyapunov method, is exploited to establish a delay-independent sufficient condition for the exponential stability of stochastic Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms. Moreover, for the deterministic delayed Cohen–Grossberg neural networks, with or without reaction–diffusion terms, sufficient criteria for their global exponential stability are also obtained. The proposed results improve and extend those in the earlier literature and are easier to verify. An example is also given to illustrate the correctness of our results.     

Weak attractor for stochastic Cohen–Grossberg neural networks with delays

This paper investigates a weak attractor for stochastic Cohen–Grossberg neural networks with delays. By employing the Lyapunov method and Lasalle-type theorem, novel results, and sufficient criteria on the weak attractor are obtained.     

Stability and almost periodicity for delayed high-order Hopfield neural networks with discontinuous activations

In this paper, the stability and almost periodicity for delayed high-order Hopfield neural networks with discontinuous activations are investigated. Some new criteria ensuring the existence and global exponential stability of almost periodic solution for the considered neural network model are established by employing the differential inclusion theory, differential inequality technique, and Lyapunov functional approach, the results of this paper improve and complement previously known results. Finally, examples with numerical simulations are presented to demonstrate the effectiveness of theoretical results.     

GLOBAL ASYMPTOTIC STABILITY CONDITIONS OF DELAYED NEURAL NETWORKS

1　IntroductionandProblemEductionRecently,thestudiesofthestabilityforcellularneuralnetworks (CNNs)anddelayedcellularneuralnetworks (DCNNs)haveattractedattentionsofresearchersandseveralimportantresultshavebeenobtained .MostpapersdealtwithcompletelystableCNNsandDCNNsthataresuitableforimageprocessingapplications.CNNshavebeenwidelyappliedtoimageprocessing ,toprocessmovingimages,onemustintroducedelaysinthesignalstransmittedamongthecells.Buttimedelaysmayleadtoanoscillationphenomenonand ,furt…     

GLOBAL DYNAMICS OF DELAYED BIDIRECTIONAL ASSOCIATIVE MEMORY （BAM） NEURAL NETWORKS

IntroductionConsiderthebidirectionalassociativememory (BAM )neuralnetworkswithconstanttransmissiondelaysdescribedbyasystemofdelaydifferentialequationsoftheform[1,2 ]:dxi(t)dt =-aixi(t) nj=1bijfj(yj(t-σij) ) Ii,　　i=1 ,2 ,… ,m ,dyj(t)dt =-cjyj(t) mi=1djigi(xi(t-τji) ) Jj,　　j=1 ,2 ,… ,n ,fort >0 .Thesystem ( 1 )consistsoftwosetsofneurons (orunits)arrangedontwolayers,namely ,I_layerandJ_layer.Inthesystem ( 1 ) ,xi( ·)andyj( ·)denotemembranepotentialoftheithneuronsfromtheI_laye…     

Exponential synchronization of chaotic neural networks with time delays: a <Emphasis Type="Italic">M</Emphasis>-matrix approach

Based on M-matrix theory, global exponential synchronization of a class of time-varying delayed chaotic neural networks is investigated. Without designing a Lyapunov function, some new criteria are established under less restrictive conditions using this approach. Finally, simulation examples are given to verify the effectiveness of the obtained conditions.