Global Exponential Robust Stability of High-Order Hopfield Neural Networks with S-Type Distributed Time Delays

Zheng, Haiyong; Wu, Bin; Wei, Tengda; Wang, Linshan; Wang, Yangfan

doi:10.1155/2014/705496

Cited by 3 publications

(2 citation statements)

References 35 publications

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“…In the studies about global stability of neural networks models, discrete and continuous, it is usually assumed that the activation functions, f j , are Lipschitz [2,6,7,10,12,25,37]. Here we do not assume that f j are Lipschitz and hypothesis (H1) only implies the continuity of f j at u = 0.…”

Section: Remarkmentioning

confidence: 99%

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Global exponential stability of discrete-time Hopfield neural network models with unbounded delays

Oliveira

2022

Journal of Difference Equations and Applications

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In this paper, a general setting is presented to study the exponential stability of discrete-time systems with bounded or unbounded delays. Based on the M-matrix theory, we establish sufficient conditions to ensure the global exponential stability of the zero equilibrium of low-order, and high-order, discrete-time Hopfield neural network models with unbounded delays and delay in the leakage terms. A comparison of the literature shows that our results generalize and improve some in recent publications.

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Section: Remarkmentioning

confidence: 99%

“…. , a n ), B = [b ij ], δ i : Z → N 0 , and f j , g j : R → R have the same meanings as in model (19), R ∈ N, c The discrete-time model ( 25) looks like the discrete version of the continuous-time high-order Hopfield neural network model with S-type distributed delays studied in [37].…”

Section: High-order Hopfield Modelmentioning

confidence: 99%

Global exponential stability of discrete-time Hopfield neural network models with unbounded delays

Oliveira

2022

Journal of Difference Equations and Applications

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Stability and Synchronization of a Fractional Neutral Higher-Order Neural Network System

Tatar

2020

International Journal of Nonlinear Sciences and Numerical Simulation

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We discuss the stability and synchronization of some neural network systems with more than one feature. They are of higher-order, of fractional order and also involving delays of neutral type. Each one of these features presents substantial difficulties to overcome. We prove stability and synchronization of Mittag-Leffler type. This rate is fairly reasonable in case of fractional order. This leads us to prove a neutral fractional version of the well-known Halanay inequality which is interesting by itself. Another feature of the present work is the treatment of unbounded activation functions. The condition of uniform boundedness of the activation functions was commonly used in the literature.

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Finite-time and global Mittag-Leffler stability of fractional-order neural networks with S-type distributed delays

Liu,

Zuo,

2024

MATH

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<abstract><p>This paper was mainly concerned with the stability analysis of a class of fractional-order neural networks with S-type distributed delays. By using the properties of Riemann-Liouville fractional-order derivatives and integrals, along with the additivity of integration intervals and initial conditions, fractional-order integrals of the state function with S-type distributed delays were transformed into fractional-order integrals of the state function without S-type distributed delays. By virtue of the theory of contractive mapping and the Bellman-Gronwall inequality, the sufficient conditions for finite-time stability and global Mittag-Leffler stability were obtained when certain conditions were satisfied. Moreover, the correctness and realizability of the conclusion were verified through the presentation of two illustrative numerical simulation examples.</p></abstract>

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Global Exponential Robust Stability of High-Order Hopfield Neural Networks with S-Type Distributed Time Delays

Abstract: By employing differential inequality technique and Lyapunov functional method, some criteria of global exponential robust stability for the high-order neural networks with S-type distributed time delays are established, which are easy to be verified with a wider adaptive scope.

Cited by 3 publications

References 35 publications

Global exponential stability of discrete-time Hopfield neural network models with unbounded delays

Global exponential stability of discrete-time Hopfield neural network models with unbounded delays

Stability and Synchronization of a Fractional Neutral Higher-Order Neural Network System

Finite-time and global Mittag-Leffler stability of fractional-order neural networks with S-type distributed delays

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