Stability analysis of memristor-based fractional-order neural networks with different memductance functions

Cognitive Neurodynamics - In this paper, the problem of the existence, uniqueness and uniform stability of memristor-based fractional-order neural networks (MFNNs) with two different types of...     

Mean square stability of uncertain stochastic BAM neural networks with interval time-varying delays

The robust asymptotic stability analysis for uncertain BAM neural networks with both interval time-varying delays and stochastic disturbances is considered. By using the stochastic analysis approach, employing some free-weighting matrices and introducing an appropriate type of Lyapunov functional which takes into account the ranges for delays, some new stability criteria are established to guarantee the delayed BAM neural networks to be robustly asymptotically stable in the mean square. Unlike the most existing mean square stability conditions for BAM neural networks, the supplementary requirements that the time derivatives of time-varying delays must be smaller than 1 are released and the lower bounds of time varying delays are not restricted to be 0. Furthermore, in the proposed scheme, the stability conditions are delay-range-dependent and rate-dependent/independent. As a result, the new criteria are applicable to both fast and slow time-varying delays. Three numerical examples are given to illustrate the effectiveness of the proposed criteria.     

New stability criteria for uncertain neural networks with interval time-varying delays

This paper is concerned with the stability analysis for neural networks with interval time-varying delays and parameter uncertainties. An approach combining the Lyapunov-Krasovskii functional with the differential inequality and linear matrix inequality techniques is taken to investigate this problem. By constructing a new Lyapunov-Krasovskii functional and introducing some free weighting matrices, some less conservative delay-derivative-dependent and delay-derivative-independent stability criteria are established in term of linear matrix inequality. And the new criteria are applicable to both fast and slow time-varying delays. Three numerical examples show that the proposed criterion are effective and is an improvement over some existing results in the literature.     

Delay-dependent robust exponential stability for uncertain recurrent neural networks with time-varying delays

This paper considers the problem of robust exponential stability for a class of recurrent neural networks with time-varying delays and parameter uncertainties. The time delays are not necessarily differentiable and the uncertainties are assumed to be time-varying but norm-bounded. Sufficient conditions, which guarantee that the concerned uncertain delayed neural network is robustly, globally, exponentially stable for all admissible parameter uncertainties, are obtained under a weak assumption on the neuron activation functions. These conditions are dependent on the size of the time delay and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed stability results.     

Dynamics of diluted attractor neural networks with delays

We present an analysis of the attractors of a deterministic dynamics in formal neural networks characterized by binary threshold units and a nonsymmetric connectivity. It is shown that in these networks a stored pattern or a pattern sequence is represented by a cloud of attractors rather than by a single attractor. Dilution, which we describe by a power-law scaling, and delayed couplings are shown to equip this type of network with a dynamic behaviour that is interesting enough for simplified models of biological motor systems. Received: 27 November 1992/Accepted in revised form: 22 September 1993     

LMI-based asymptotic stability analysis of neural networks with time-varying delays

The problem of the global asymptotic stability for a class of neural networks with time-varying delays is investigated in this paper, where the activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. By constructing suitable Lyapunov functionals and combining with linear matrix inequality (LMI) technique, new global asymptotic stability criteria about different types of time-varying delays are obtained. It is shown that the criteria can provide less conservative result than some existing ones. Numerical examples are given to demonstrate the applicability of the proposed approach.     

Global and robust stability of interval Hopfield neural networks with time-varying delays

In this paper, we investigate the problem of global and robust stability of a class of interval Hopfield neural networks that have time-varying delays. Some criteria for the global and robust stability of such networks are derived, by means of constructing suitable Lyapunov functionals for the networks. As a by-product, for the conventional Hopfield neural networks with time-varying delays, we also obtain some new criteria for their global and asymptotic stability.     

Stability and synchronization analysis of inertial memristive neural networks with time delays

This paper is concerned with the problem of stability and pinning synchronization of a class of inertial memristive neural networks with time delay. In contrast to general inertial neural networks, inertial memristive neural networks is applied to exhibit the synchronization and stability behaviors due to the physical properties of memristors and the differential inclusion theory. By choosing an appropriate variable transmission, the original system can be transformed into first order differential equations. Then, several sufficient conditions for the stability of inertial memristive neural networks by using matrix measure and Halanay inequality are derived. These obtained criteria are capable of reducing computational burden in the theoretical part. In addition, the evaluation is done on pinning synchronization for an array of linearly coupled inertial memristive neural networks, to derive the condition using matrix measure strategy. Finally, the two numerical simulations are presented to show the effectiveness of acquired theoretical results.     

Global asymptotic stability of complex-valued neural networks with additive time-varying delays

In this paper, we extensively study the global asymptotic stability problem of complex-valued neural networks with leakage delay and additive time-varying delays. By constructing a suitable Lyapunov–Krasovskii functional and applying newly developed complex valued integral inequalities, sufficient conditions for the global asymptotic stability of proposed neural networks are established in the form of complex-valued linear matrix inequalities. This linear matrix inequalities are efficiently solved by using standard available numerical packages. Finally, three numerical examples are given to demonstrate the effectiveness of the theoretical results.     

Exponential input-to-state stability of recurrent neural networks with multiple time-varying delays

In this paper, input-to-state stability problems for a class of recurrent neural networks model with multiple time-varying delays are concerned with. By utilizing the Lyapunov–Krasovskii functional method and linear matrix inequalities techniques, some sufficient conditions ensuring the exponential input-to-state stability of delayed network systems are firstly obtained. Two numerical examples and its simulations are given to illustrate the efficiency of the derived results.     

Attractability and location of equilibrium point of cellular neural networks with time-varying delays

This paper presents new theoretical results on global exponential stability of cellular neural networks with time-varying delays. The stability conditions depend on external inputs, connection weights and delays of cellular neural networks. Using these results, global exponential stability of cellular neural networks can be derived, and the estimate for location of equilibrium point can also be obtained. Finally, the simulating results demonstrate the validity and feasibility of our proposed approach.     

Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays

This paper investigates the finite-time synchronization and fixed-time synchronization problems of inertial memristive neural networks with time-varying delays. By utilizing the Filippov discontinuous theory and Lyapunov stability theory, several sufficient conditions are derived to ensure finite-time synchronization of inertial memristive neural networks. Then, for the purpose of making the setting time independent of initial condition, we consider the fixed-time synchronization. A novel criterion guaranteeing the fixed-time synchronization of inertial memristive neural networks is derived. Finally, three examples are provided to demonstrate the effectiveness of our main results.     

Robust delay-dependent stability of uncertain inertied neural networks with impulsive effects and distributed-delay

The robust stability problem of uncertain inertial neural networks with impulsive effects and distributed-delay is considered in the present paper.The average impulsive interval and differential inequality for delay differential equations are used to obtain the global exponential stability of the inertial neural networks.The robust distributed-delaydependent stability criteria here are proposed in terms of both linear matrix inequalities and algebraic inequalities.Our results can not only be used to obtain the stability of the uncertain inertial neural network with impulsive disturbance,but also be utilized to design the impulsive control for the uncertain inertial neural networks.The novel criteria complement and extend the previous works on uncertain inertial neural network with/without impulsive effects.Typical numerical examples are used to test the validity of the developed stability criteria finally.     

Sequences of smoothly correlated patterns in neural networks with random transmission delays

A neural network with a broad distribution of transmission delays was used to study numerically the retrieval of sequences having several types of correlations between successive patterns. In the case of sequences consisting of patterns correlated for finite time, the quality of retrieval was found to be (more or less) independent of the pattern correlation width and the delay distribution. On the other hand the quality of retrieval is dependent on these factors in the case of sequences with pattern correlation functions with long time tails. Finally we have studied to what extent the storage capacity depends on the pattern correlation function and the delay distribution.     

Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays

In this article, we consider a class of neutral impulsive shunting inhibitory cellular neural networks with time varying coefficients and leakage delays. We study the existence and the exponential stability of the piecewise differentiable pseudo almost-periodic solutions and establish sufficient conditions for the existence and exponential stability of such solutions. An example is provided to illustrate the theory developed in this work.     

Exponential synchronization for fuzzy cellular neural networks with time-varying delays and nonlinear impulsive effects

In this paper, the globally exponential synchronization of delayed fuzzy cellular neural networks with nonlinear impulsive effects are concerned. By utilizing inequality techniques and Lyapunov functional method, some sufficient conditions on the exponential synchronization are obtained based on p-norm. Finally, a simulation example is given to illustrate the effectiveness of the theoretical results.     

New criteria of almost periodic solution for bam neural networks with delays and impulsive effects

This paper presents some sufficient conditions for the existence and global exponential stability of the almost periodic solution for impulsive bi-directional associative memory neural networks with time-varying delays by using Lyapunov functional and Gronwall-Bellmans inequality technique. Comparing with known literatures, the results of this paper are new and they complement previously known results.     

Biochemical networks with uncertain parameters

The modelling of biochemical networks becomes delicate if kinetic parameters are varying, uncertain or unknown. Facing this situation, we quantify uncertain knowledge or beliefs about parameters by probability distributions. We show how parameter distributions can be used to infer probabilistic statements about dynamic network properties, such as steady-state fluxes and concentrations, signal characteristics or control coefficients. The parameter distributions can also serve as priors in Bayesian statistical analysis. We propose a graphical scheme, the 'dependence graph', to bring out known dependencies between parameters, for instance, due to the equilibrium constants. If a parameter distribution is narrow, the resulting distribution of the variables can be computed by expanding them around a set of mean parameter values. We compute the distributions of concentrations, fluxes and probabilities for qualitative variables such as flux directions. The probabilistic framework allows the study of metabolic correlations, and it provides simple measures of variability and stochastic sensitivity. It also shows clearly how the variability of biological systems is related to the metabolic response coefficients.     

A novel global exponential stability result for discrete-time cellular neural networks with variable delays

Global exponential stability is considered for a class of discrete-time cellular neural networks with variable delays. By employing a discrete Halanay inequality, a new result is presented ensuring global exponential stability of the unique equilibrium point of the networks. The result extends and improves the earlier publications due to the fact that it removes some restrictions on the delay. An example is given to illustrate the effectiveness of the global exponential stability condition provided here.     

New criteria on global exponential stability of bam neural networks with distributed delays and reaction-diffusion terms

This paper presents new theoretical results on global exponential stability of bi-directional associative memory neural networks with distributed delays and reaction-diffusion terms based on the inequality technique, Lyapunov functional, and analysis technique. The results remove the usual assumption that the activation functions are of monotonous or differential character. Exponential converging velocity index is estimated, which depends on the delay kernel functions and system parameters. Finally, two numerical examples are given to show the validity and feasibility of our results.