Delay-dependent Criteria for Robust Stability of Uncertain Switched Hopfield Neural Networks

This paper deals with the problem of delay-dependent robust stability for a class of switched Hopfield neural networks with time-varying structured uncertainties and time-varying delay. Some Lyapunov-KrasoVskii functionals are constructed and the linear matrix inequality （LMI） approach and free weighting matrix method are employed to devise some delay-dependent stability criteria which guarantee the existence, uniqueness and global exponential stability of the equilibrium point for all admissible parametric uncertainties. By using Leibniz-Newton formula, free weighting matrices are employed to express this relationship, which implies that the new criteria are less conservative than existing ones. Some examples suggest that the proposed criteria are effective and are an improvement over previous ones.

Existence and Exponential Stability of Almost Periodic Solution for Hopfield Neural Network Equations with Almost Periodic Imput

By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. Irt this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures.

Robust stability for stochastic interval delayed Hopfield neural networks

A type of stochastic interval delayed Hopfield neural networks as du(t) = [-AIu(t) + WIf(t,u(t)) + WIτf7τ(uτ(t)] dt +σ(t, u(t), uτ(t)) dw(t) on t≥0 with initiated value u(s) = ζ(s) on - τ≤s≤0 has been studied. By using the Razumikhin theorem and Lyapunov functions, some sufficient conditions of their globally asymptotic robust stability and global exponential stability on such systems have been given. All the results obtained are generalizations of some recent ones reported in the literature for uncertain neural networks with constant delays or their certain cases.

New Delay-dependent Global Asymptotic Stability Condition for Hopfield Neural Networks with Time-varying Delays

This paper deals with the global asymptotic stability problem for Hopfield neural networks with time-varying delays. By resorting to the integral inequality and constructing a Lyapunov-Krasovskii functional, a novel delay-dependent condition is established to guarantee the existence and global asymptotic stability of the unique equilibrium point for a given delayed Hopfield neural network. This criterion is expressed in terms of linear matrix inequalities （LMIs）, which can be easily checked by utilizing the recently developed algorithms for solving LMIs. Examples are provided to demonstrate the effectiveness and reduced conservatism of the proposed condition.

Stability of discrete Hopfield neural networks with delay

Discrete Hopfield neural network with delay is an extension of discrete Hopfield neural network. As it is well known, the stability of neural networks is not only the most basic and important problem but also foundation of the network＇s applications. The stability of discrete HJopfield neural networks with delay is mainly investigated by using Lyapunov function. The sufficient conditions for the networks with delay converging towards a limit cycle of length 4 are obtained. Also, some sufficient criteria are given to ensure the networks having neither a stable state nor a limit cycle with length 2. The obtained results here generalize the previous results on stability of discrete Hopfield neural network with delay and without delay.

GLOBAL ATTRACTIVITY AND GLOBAL EXPONENTIAL STABILITY FOR DELAYED HOPFIELD NEURAL NETWORK MODELS

Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constructing suitable Liapunov function, some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural network,; with time delays are presented.

GLOBAL STABILITY IN HOPFIELD NEURAL NETWORKS WITH DISTRIBUTED TIME DELAYS

In this paper, without assuming the boundedness, monotonicity and differentiability of the activation functions, the conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of Hopfield neural network models with distributed time delays are studied. Using M-matrix theory and constructing proper Liapunov functionals, the sufficient conditions for global asymptotic stability are obtained.

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.

Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique

The global stability problem of Takagi-Sugeno（T-S） fuzzy Hopfield neural networks（FHNNs） with time delays is investigated.Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism.Firstly,using both Finsler＇s lemma and an improved homogeneous matrix polynomial technique,and applying an affine parameter-dependent Lyapunov-Krasovskii functional,we obtain the convergent LMI-based stability criteria.Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique.Secondly,to further reduce the conservatism,a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs,which is suitable to the homogeneous matrix polynomials setting.Finally,two illustrative examples are given to show the efficiency of the proposed approaches.

New Results of Global Asymptotical Stability for Impulsive Hopfield Neural Networks with Leakage Time-Varying Delay

In this paper, Hopfield neural networks with impulse and leakage time-varying delay are considered. New sufficient conditions for global asymptotical stability of the equilibrium point are derived by using Lyapunov-Kravsovskii functional, model transformation and some analysis techniques. The criterion of stability depends on the impulse and the bounds of the leakage time-varying delay and its derivative, and is presented in terms of a linear matrix inequality (LMI).

Coexistence behavior of asymmetric attractors in hyperbolic-type memristive Hopfield neural network and its application in image encryption

The neuron model has been widely employed in neural-morphic computing systems and chaotic circuits.This study aims to develop a novel circuit simulation of a three-neuron Hopfield neural network(HNN)with coupled hyperbolic memristors through the modification of a single coupling connection weight.The bistable mode of the hyperbolic memristive HNN(mHNN),characterized by the coexistence of asymmetric chaos and periodic attractors,is effectively demonstrated through the utilization of conventional nonlinear analysis techniques.These techniques include bifurcation diagrams,two-parameter maximum Lyapunov exponent plots,local attractor basins,and phase trajectory diagrams.Moreover,an encryption technique for color images is devised by leveraging the mHNN model and asymmetric structural attractors.This method demonstrates significant benefits in correlation,information entropy,and resistance to differential attacks,providing strong evidence for its effectiveness in encryption.Additionally,an improved modular circuit design method is employed to create the analog equivalent circuit of the memristive HNN.The correctness of the circuit design is confirmed through Multisim simulations,which align with numerical simulations conducted in Matlab.

Novel criteria for global exponential stability and periodic solutions of delayed Hopfield neural networks

The global exponentially stability and the existence of periodic solutions of a class of Hopfield neural networks with time delays are investigated. By constructing a novel Lyapunov function, new criteria are provided to guarantee the global exponentially stability of such systems. For the delayed Hopfield neural networks with time-varying external inputs, new criteria are also acquired for the existence and exponentially stability of periodic solutions. The results are generalizations and improvements of some recent achievements reported in the literature on networks with time delays.

Analysis for Robust Stability of Hopfield Neural Networks with Multiple Delays

The robust stability of a class of Hopfield neural networks with multiple delays and parameter perturbations is analyzed. The sufficient conditions for the global robust stability of equilibrium point are given by way of constructing a suitable Lyapunov functional. The conditions take the form of linear matrix inequality (LMI), so they are computable and verifiable efficiently. Furthermore, all the results are obtained without assuming the differentiability and monotonicity of activation functions. From the viewpoint of system analysis, our results provide sufficient conditions for the global robust stability in a manner that they specify the size of perturbation that Hopfield neural networks can endure when the structure of the network is given. On the other hand, from the viewpoint of system synthesis, our results can answer how to choose the parameters of neural networks to endure a given perturbation.

STABILITY ANALYSIS OF HOPFIELD NEURAL NETWORKS WITH TIME DELAY

The global asymptotic stability for Hopfield neural networks with time delay was investigated, A theorem and two corollaries were obtained, in which the boundedness and differentiability of f(j) on R in some articles were deleted. Some sufficient conditions for the existence of global asymptotic stable equilibrium of the networks in this paper are better than the sufficient conditions in quoted articles.

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.

ON THE ASYMPTOTIC BEHAVIOR OF HOPFIELD NEURAL NETWORK WITH PERIODIC INPUTS

Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neural network with periodic inputs are given by using Mawhin's coincidence degree theory and Liapunov's function method.

New results on the robust stability analysis of neural networks with discrete and distributed time delays

Delay-dependent robust stability of cellular neural networks with time-varying discrete and distributed time-varying delays is considered. Based on Lyapunov stability theory and the linear matrix inequality （LMIs） technique, delay-dependent stability criteria are derived in terms of LMIs avoiding bounding certain cross terms, which often leads to conservatism. The effectiveness of the proposed stability criteria and the improvement over the existing results are illustrated in the numerical examples.

STABILITY OF BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH DELAYS

In this paper the globally asymptotic stability of more general two-layer nonlinear feedback associative memory neural networks with time delays is examined. The sufficient conditions of existence, uniqueness and globally asymptotic stability of the equilibrum position are given. Finally, two interesting examples to illustrate the theory are given.

Nonlinear Dynamics and Stability of Neural Networks with Delay-Time

In this paper we study the dynamic properties and stabilities of neural networks with delay-time (which includes the time-varying case) by differential inequalities and Lyapunov function approaches. The criteria of connective stability, robust stability, Lyapunov stability, asymptotic atability, exponential stability and Lagrange stability of neural networks with delay-time are established, and the results obtained are very useful for the design, implementation and application of adaptive learning neural networks.

Convergence in Continuous Hopfield Neural Network with Delays

A sufficient condition are derived for the global asymptotic stability of the equilibrium of continuous Hopfield neural networks with delays of the