GLOBAL STABILITY ANALYSIS IN CELLULAR NEURAL NETWORKS WITH UNBOUNDED TIME DELAYS

Without assuming the boundedness and differentiability of the activation functions, the conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of cellular neural networks with unbounded time delays and variable delays were studied. Using the idea of vector Liapunov method, the intero-differential inequalities with unbounded delay and variable delays were constructed. By the stability analysis of the intero-differential inequalities, the sufficient conditions for global asymptotic stability of cellular neural networks were obtained.     

Dissipativity of a class of cellular neural networks with proportional delays

In this paper, the problem of dissipativity is investigated for cellular neural networks with proportional delays. Without assuming monotonicity, differentiability, and boundedness of activation functions, two new delay-independent criteria for checking the dissipativity of the addressed neural networks are established by using inner product properties and matrix theory. Two examples and their simulation results are given to show the effectiveness and less conservatism of the proposed criteria.     

GLOBAL ASYMPTOTIC STABILITY CONDITIONS OF DELAYED NEURAL NETWORKS

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

Global asymptotic stability for Hopfield-type neural networks with diffusion effects

The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium (if it exists) is globally asymptotically stable and this implies that the equilibrium of the system is unique.     

Global exponential stability for quaternion-valued recurrent neural networks with time-varying delays

Nonlinear Dynamics - In this paper, we employ a novel method for solving the problem of the global exponential stability of quaternion-valued recurrent neural networks (QVNNs) with time-varying...     

Global exponential stability of stochastic memristor-based complex-valued neural networks with time delays

In recent years, the dynamic behaviors of complex-valued neural networks have been extensively investigated in a variety of areas. This paper focuses on the stability of stochastic memristor-based complex-valued neural networks with time delays. By using the Lyapunov stability theory, Halanay inequality and Itô formula, new sufficient conditions are obtained for ensuring the global exponential stability of the considered system. Moreover, the obtained results not only generalize the previously published corresponding results as special cases for our results, but also can be checked with the parameters of system itself. Finally, simulation results in three numerical examples are discussed to illustrate the theoretical results.     

A LMI-based approach to global asymptotic stability of neural networks with time varying delays

In this paper, the asymptotic stability of neural networks with time varying delay is studied by using the nonsmooth analysis, Lyapunov functional method and linear matrix inequality (LMI) technique. It is noted that the proposed results do not require smoothness of the behaved function and activation function as well as boundedness of the activation function. Several sufficient conditions are presented to show the uniqueness and the global asymptotical stability of the equilibrium point. Also, a high-dimensional matrix condition to ensure the uniqueness and the global asymptotical stability of equilibrium point can be reduced to a low-dimensional condition. The obtained results are easy to apply and improve some earlier works. Finally, we give two simulations to justify the theoretical analysis in this paper. This work was supported by the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2006093.     

Generalized LMI-based approach to global asymptotic stability of cellular neural networks with delay

A global asymptotic stability problem of cellular neural networks with delay is investigated. A new stability condition is presented based on the Lyapunov-Krasovskii method, which is dependent on the amount of delay. A result is given in the form of a linear matrix inequality, and the admitted upper bound of the delay can be easily obtained. The time delay dependent and independent results can be obtained, which include some previously published results. A numerical example is given to show the effectiveness of the main results.     

Global Mittag-Leffler stability and synchronization of impulsive fractional-order neural networks with time-varying delays

In this paper we consider a class of impulsive Caputo fractional-order cellular neural networks with time-varying delays. Applying the fractional Lyapunov method and Mittag-Leffler functions, we give sufficient conditions for global Mittag-Leffler stability which implies global asymptotic stability of the network equilibrium. Our results provide a design method of impulsive control law which globally asymptotically stabilizes the impulse free fractional-order neural network time-delay model. The synchronization of fractional chaotic networks via non-impulsive linear controller is also considered. Illustrative examples are given to demonstrate the effectiveness of the obtained results.     

GLOBAL EXPONENTIAL STABILITY OF HOPFIELD NEURAL NETWORKS WITH VARIABLE DELAYS AND IMPULSIVE EFFECTS

A class of Hopfield neural network with time-varying delays and impulsive effects is concerned. By applying the piecewise continuous vector Lyapunov function some sufficient conditions were obtained to ensure the global exponential stability of impulsive delay neural networks. An example and its simulation are given to illustrate the effectiveness of the results.     

Global stability and stabilization for inertial memristive neural networks with unbounded distributed delays

Nonlinear Dynamics - This paper investigates the stability and stabilization of inertial memristive neural networks (IMNNs) with discrete and unbounded distributed delays. The considered IMNNs are...     

The stability in neural networks with interneuronal transmission delays

1.IntroductionInthispaper,westudythefollowingmodelofaneuralwithnunits:inwhichfi(t)correspondstothemembranepotentialofthei-thunitattimet;h(xj)denotestheconversionofthemembranepotentialofthe.l-thunitsintoitsfiringrate:coildellotesthestrengthofthej-thunit;accorrespondStothetransmissiondelayalongtheaxonofthe.j-thunit;theConstantpid,enotestheexternalbiasorclampedinputfi-omoutsidethenetworktothei-thunit:hirepresentstheratewithwhichtheI-thLlnltwillresetitspotentialtotherestingstateinisolationwhendis…     

Robust stability of a class of neural networks with time delays

A stability analysis of the equilibrium position for a given class of Hopfield neural networks with time delays is presented. The robustness of the equilibrium stability with respect to variations in the time delays, system parameters, and interconnection matrix is analyzed. Three approaches are presented which account in various ways for stability of the equilibrium with respect to these perturbations.Work conducted while visiting the University of Bremen, supported by the Deutscheforschungsgemeinschaft.     

Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays

In this paper, the problem of finite-time stability of fractional-order complex-valued memristor-based neural networks (NNs) with time delays is extensively investigated. We first initiate the fractional-order complex-valued memristor-based NNs with the Caputo fractional derivatives. Using the theory of fractional-order differential equations with discontinuous right-hand sides, Laplace transforms, Mittag-Leffler functions and generalized Gronwall inequality, some new sufficient conditions are derived to guarantee the finite-time stability of the considered fractional-order complex-valued memristor-based NNs. In addition, some sufficient conditions are also obtained for the asymptotical stability of fractional-order complex-valued memristor-based NNs. Finally, a numerical example is presented to demonstrate the effectiveness of our theoretical results.     

Improved delay-dependent stability conditions for recurrent neural networks with multiple time-varying delays

This paper investigates the global asymptotic stability problem for recurrent neural networks with multiple time-varying delays. Using the free-weighting matrix technique, and incorporating the interconnected information between the upper bounds of multiple time-varying delays, two less conservative delay-dependent asymptotic stability conditions are proposed, which are expressed by linear matrix inequalities, and can be conveniently solved by the existing softwares. Numerical examples show the reduce conservatism of the obtained conditions.     

Delay-independent stability criteria for complex-valued BAM neutral-type neural networks with time delays

This paper focuses on the global asymptotic stability of complex-valued bidirectional associative memory (BAM) neutral-type neural networks with time delays. By virtue of homeomorphism theory, inequality techniques and Lyapunov functional, a set of delay-independent sufficient conditions is established for assuring the existence, uniqueness and global asymptotic stability of an equilibrium point of the considered complex-valued BAM neutral-type neural network model. The assumption on boundedness of the activation functions is not required, and the LMI-based criteria are easy to be checked and executed in practice. Finally, we give one example with simulation to show the applicability and effectiveness of our main results.     

Robust exponential stability for interval neural networks with delays and non-Lipschitz activation functions

In this paper, the global robust exponential stability of interval neural networks with delays and inverse Hölder neuron activation functions is considered. By using linear matrix inequality (LMI) techniques and Brouwer degree properties, the existence and uniqueness of the equilibrium point are proved. By applying Lyapunov functional approach, a sufficient condition which ensures that the network is globally robustly exponentially stable is established. A numerical example is provided to demonstrate the validity of the theoretical results.     

Global stability in switched recurrent neural networks with time-varying delay via nonlinear measure

In this paper, based on switched systems and recurrent neural networks (RNNs) with time-varying delay, the model of switched RNNs is formulated. Global asymptotical stability (GAS) and global robust stability (GRS) for such switched neural networks are studied by employing nonlinear measure and linear matrix inequality (LMI) techniques. Some new sufficient conditions are obtained to ensure GAS or GRS of the unique equilibrium of the proposed switched system. Furthermore, the proposed LMI results are computationally efficient as it can be solved numerically with standard commercial software. Finally, three examples are provided to illustrate the usefulness of the 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.     

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.