Stability Of Hopfield Neural Networks Research Articles

Stability of Hopfield neural network with resistive and magnetic coupling

Inspired by the interplay between both electrical and chemical synapses, we propose an analog electronic synapse-like model to characterize biological synaptic properties. By introducing the resistive and magnetic coupling, we consider hierarchical interconnection and the mixed couplings with two different kinds of coupling mechanisms. Meanwhile, based on Lyapunov function of the variable gradient method, stability of the Hopfield neural network with resistive and magnetic couplings was derived as the interconnection is symmetric and asymmetric, respectively. Furthermore, corresponding examples are calculated by using the numerical approach. The obtained results can be helpful to further develop brain-like systems based on the hierarchical Hopfield neural network with timing-dependent synaptic plasticity.

A new criterion of asymptotic stability for Hopfield neural networks with time-varying delay

The objective of this paper is to analyze the stability of Hopfield neural networks with time-varying delay. For the system to operate in a steady state, it is important to guarantee the stability of Hopfield neural networks with time-varying delay. The Lyapunov-Krasovsky functional method is the main method for investigating the stability of time-delayed systems. On the basis of this method, the stability of Hopfield neural networks with time-varying delay is ana-lysed. It is known that due to such factors as communication time, limited switching speed of various active devices, time delays often arise in various technical systems, which significantly degrade the performance of the system, which can in turn lead to a complete loss of stability. In this regard, a Lyapunov-Krasovsky type delay-product functional was con-structed in the paper, which allows more information about the time delay and reduces the conservatism of the method. Then a generalized integral inequality based on the free matrix was used. A new criterion for asymptotic stability of Hop-field neural networks with time-varying delay, which has less conservatism, was formulated. The effectiveness of the proposed method is illustrated. Thus an asymptotic stability criterion for Hopfield neural networks with time-varying delay was formulated and justified. The expanded Lyapunov-Krasovsky functional is constructed on the basis of delay and quadratic multiplicative functional, and the derivative of the functional is defined by a matrix integral inequality with free weights. The effectiveness of the method is illustrated by a model example.

Robustness of Hopfield Neural Networks Described by Differential Algebraic Systems of Index-1 under the Conditions of Deviation Argument and Stochastic Disturbance

Robustness refers to the ability of a system to maintain its original state under a continuous disturbance conditions. The deviation argument (DA) and stochastic disturbances (SDs) are enough to disrupt a system and keep it off course. Therefore, it is of great significance to explore the interval length of the deviation function and the intensity of noise to make a system remain exponentially stable. In this paper, the robust stability of Hopfield neural network (VPHNN) models based on differential algebraic systems (DAS) is studied for the first time. By using integral inequalities, expectation inequalities, and the basic control theory method, the upper bound of the interval of the deviation function and the noise intensity are found, and the system is guaranteed to remain exponentially stable under these disturbances. It is shown that as long as the deviation and disturbance of a system are within a certain range, there will be no unstable consequences. Finally, several simulation examples are used to verify the effectiveness of the approach and are described below.

Exponential stability of Hopfield neural networks with conformable fractional derivative

A class of Hopfield neural networks with conformable fractional derivative is studied. Sufficient conditions are derived for the existence and uniqueness of the equilibrium point of the network. Moreover, by using a Lyapunov function exponential stability result is proved.

Exponential stability of Hopfield neural networks of neutral type with multiple time-varying delays

<abstract> This paper investigates the problem for exponential stability of Hopfield neural networks of neutral type with multiple time-varying delays. Different from the existing results, the states of the neurons involve multiple time-varying delays and time derivative of states of neurons also include multiple time-varying delays. The exponential stability of such neutral-type system has not been received enough attention since it is not easy to construct a suitable Lyapunov-Krasovskii functional to analyze the exponential stability of this type of neural system. Novel sufficient conditions of the exponential stability are established by using Lyapunov method and inequality techniques. Compared with some references, the mathematical expression of the neutral-type system is more general and the established algebraic conditions are less conservative. Three examples are given to demonstrate the effectiveness of the theoretical results and compare the established stability conditions to the previous results. </abstract>

Generalized norm for existence, uniqueness and stability of Hopfield neural networks with discrete and distributed delays

In this paper, the existence, uniqueness and stability criteria of solutions for Hopfield neural networks with discrete and distributed delays (DDD HNNs) are investigated by the definitions of three kinds of generalized norm (ξ-norm). A general DDD HNN model is firstly introduced, where the discrete delays τpq(t) are asynchronous time-varying delays. Then, {ξ,1}-norm, {ξ,2}-norm and {ξ,∞}-norm are successively used to derive the existence, uniqueness and stability criteria of solutions for the DDD HNNs. In the proof of theorems, special functions and assumptions are given to deal with discrete and distributed delays. Furthermore, a corollary is concluded for the existence and stability criteria of solutions. The methods given in this paper can also be used to study the synchronization and μ-stability of different DDD NNs. Finally, two numerical examples and their simulation figures are given to illustrate the effectiveness of these results.

基于Gronwall积分不等式的Hopfield神经网络稳定性的新判据

基于Gronwall积分不等式的Hopfield神经网络稳定性的新判据

Nonuniform behavior and stability of Hopfield neural networks with delay

Based on a new abstract result on the behavior of nonautonomous delayed equations, we obtain a stability result for the solutions of a general discrete nonautonomous Hopfield neural network model with delay. As an application we improve some existing results on the stability of Hopfield models.

Stability of Hopfield Neural Networks with Delay and Piecewise Constant Argument

Stability of Hopfield Neural Networks with Delay and Piecewise Constant Argument

Analysis of Stability of Hopfield Neural Networks and Design of Impulsive Controller

Based on the proper Lyapunov functions and the Riccati liner inequality, the Robust H-stability of Hopfield neural networks with impulsive effects is studied and some sufficient conditions for robust H-stability are established, the impulsive stabilization criteria can be verified by the impulsive controller, simulation validate the main results.

Global robust exponential stability for Hopfield neural networks with non-Lipschitz activation functions

We consider the problem of global robust exponential stability for Hopfield neural networks with norm-bounded parameter uncertainties and inverse Holder neuron activation functions. By using the Brouwer degree properties and some analysis techniques, we investigate the existence and uniqueness of an equilibrium point. Based on the Lyapunov stability theory, we derive a global robust exponential-stability criterion in terms of a linear matrix inequality (LMI). Two numerical examples are provided to demonstrate the efficiency and validity of the proposed robust stability results.

Stability of Hopfield neural networks with time delays and variable-time impulses

The stability of Hopfield neural networks with fixed-time impulses has been intensively investigated in recent years. However, few existing publications addressed the stability of delayed neural networks with variable-time impulses. In this paper, we consider the case of variable-time impulses and attempt to establish the general stability criteria. It shows that the proposed results can also be applied to the case of fixed-time impulses, which provide a new stability condition for the case of fixed-time impulses. To illustrate the effectiveness of our theoretical results, numerical examples and simulations are also presented.

Exponential stability of Hopfield neural networks with impulses

For a Hopfield neural network with periodic coefficients, a new criterion is proposed to obtain the existence of a periodic solution and its exponential stability. Our assumptions are in the form of inequalities involving integral averages and the assigned jumps.

Exponential stability of Hopfield neural networks with time-varying delays via impulsive control

In this paper, by utilizing the Lyapunov functionals, the analysis method and the impulsive control, we analyze the exponential stability of Hopfield neural networks with time-varying delays. A new criterion on the exponential stabilization by impulses and the exponential stabilization by periodic impulses is gained. We can see that impulses do contribution to the system's exponential stability. Two examples are given to illustrate the effectiveness of our result. Copyright © 2010 John Wiley & Sons, Ltd.

Novel delay-dependent global asymptotic stability condition of Hopfield neural networks with delays

In this paper, the global asymptotic stability of Hopfield neural networks with delays is investigated. Distinct differences from other analytical approaches lie in transforming to an equivalent system by using a parameterized transformation which allows free variables in an operator. A novel, less conservative and restrictive criterion than those established in the earlier references is given in terms of several matrix inequalities by utilizing the Lyapunov theory and matrix inequality framework. The results are related to the size of delays. Numerical examples are given to show the effectiveness of our proposed method.

Complex dynamics and stability of Hopfield neural networks with delays

In this paper, by utilising the Lyapunov functional method, we analyse the global asymptotic stability of Hopfield neural networks with delays. We obtain some new sufficient conditions to ensure the global asymptotic stability of the model being independent of delays. By using the Lyapunov second method for special cases, we also get that the equilibrium of the system is locally asymptotically stable when the delay is under a critical value; and when the delay is equal to this value, Hopf bifurcation will occur and the equilibrium is unstable; and when the delay is above the critical value, the system will demonstrate complex dynamics. Finally, numerical simulations are presented to verify the analytical results.

Delay-dependent robust stability for Hopfield neural networks of neutral-type

In this paper, the problem of delay-dependent robust stability for Hopfield neural networks of neutral-type is investigated. The neural networks system considered is different from the others, which has time-varying delays in neutral and discrete terms. A new class of Lyapunov–Krasovskii functional combines with the descriptor model transformation to ensure a large upper bound for time delay. The delay-dependent robust stability criterion is formulated in terms of linear matrix inequalities, in which the restriction of the derivative of time-varying delay in discrete terms is removed. Since both the neutral-delays and discrete-delays are taken into account, so the obtained criterion is more general than some existing ones. Numerical examples are given to illustrate the effectiveness of the proposed methods.

Global exponential stability of Hopfield neural networks with delays and inverse Lipschitz neuron activations

This paper introduces a new class of functions called inverse Lipschitz functions ( I L ). By using I L , a novel class of neural networks with inverse Lipschitz neuron activation functions is presented. By the topological degree theory and matrix inequality techniques, the existence and uniqueness of equilibrium point for the neural network are investigated. By constructing appropriate Lyapunov functions, a sufficient condition ensuring global exponential stability of the neural network is given. At last, two numerical examples are given to demonstrate the effectiveness of the results obtained in this paper.

Global exponential stability of Hopfield neural networks with distributed delays

In this paper, dynamical behaviors of Hopfield neural networks system with distributed delays were studied. By using contraction mapping principle and differential inequality technique, a sufficient condition was obtained to ensure the existence uniqueness and global exponential stability of the equilibrium point for the model. Here we point out that our methods, which are different from previous known results, base on the contraction mapping principle and inequality technique. Two remarks were also worked out to demonstrate the advantage of our results.

New delay-dependent global asymptotic stability criteria of delayed Hopfield neural networks

In this paper, the global asymptotic stability of Hopfield neural networks (HNNs) with delays is investigated by utilizing Lyapunov functional method and the linear matrix inequality (LMI) technique. Distinct difference from other analytical approaches lies in “linearization” of the neural network model, by which the considered neural network model is transformed into a linear time-variant system. Then, a process, which is called parameterized first-order model transformation, is used to transform the linear system. Novel criteria for global asymptotic stability of the unique equilibrium point of delayed HNNs are obtained. The results are related to the size of delays. The obtained results are less conservative and restrictive than those established in the earlier references. Two numerical examples are given to show the effectiveness of our proposed method.