Stability analysis of hybrid stochastic delayed Cohen-Grossberg neural networks with Lévy noise and Markov switching

Yu, Peilin; Deng, Feiqi; Cheng, Pei

doi:10.1016/j.jfranklin.2022.05.025

Cited by 7 publications

(2 citation statements)

References 30 publications

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“…Up to the present, most of the characteristics of artificial NNs are first-order differential equations, some familiar NNs include the Cohen-Grossberg NNs [1][2][3][4], recurrent NNs [5][6][7], and Hopfield NNs [8][9][10][11]. Research on artificial NNs has been extensively concerned and achieved multitudinous results.…”

Section: Introductionmentioning

confidence: 99%

Laplace transform and nonlinear control design for quasi‐projective synchronization for Caputo inertial delayed neural networks

Zhang

Chen

et al. 2023

Math Methods in App Sciences

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The quasi‐projective synchronization problems for Caputo inertial neural networks (INNs) with delays are analyzed in this article. The considered model is transformed into two subsystems by selecting a suitable variable substitution. To realize synchronization, a novel fractional differential inequality is established, and the new lemma is derived via Laplace transform. Applying the given lemmas and inequality techniques, the synchronization conditions are inferred through different nonlinear feedback controllers. From the derivation of the theorems, it can be seen that the designed controllers are more extensive and efficacious. Furthermore, the error bound is validly estimated, and the validity of obtained theorems is illustrated by the numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Laplace transform and nonlinear control design for quasi‐projective synchronization for Caputo inertial delayed neural networks

Zhang

Chen

et al. 2023

Math Methods in App Sciences

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“…For example, experts often use Lévy noise to simulate large-scale external or internal disturbances in financial markets [3,4]. In recent years, many valuable theoretical and application results have been provided on stability for stochastic differential systems with Lévy noise [5,6]. For example, the condition of judgment for mean-square exponential stability is obtained in [7] for neural networks.…”

Section: Introductionmentioning

confidence: 99%

Delay-Independent Stability of Stochastic Systems with Time-Varying Delay and Lévy Noise

Zhang,

Liu,

Fang

et al. 2023

Advances in Transdisciplinary Engineering

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This paper focuses upon delay-independent stability for stochastic differential systems with time-varying delay driven by Lévy noise. Mainly, in view of Lyapunov function, generalized Itô’s formula and reduction to absurdity, sufficient conditions are given to obtain the delay-independent stability and mean-square exponential stability. Furthermore, due to effectiveness of the demonstration method, in this paper stability criterion for time-varying systems does not require derivative for time-varying function to be less than one, which contributes to the demonstration of delay-independent stability.

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Exponential Stability of Impulsive Stochastic Neutral Neural Networks with Lévy Noise Under Non-Lipschitz Conditions

Ma,

Li,

Liu

et al. 2024

Neural Process Lett

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In this paper, the exponential stability issue of stochastic impulsive neutral neural networks driven by Lévy noise is explored. By resorting to the Lyapunov-Krasovskii function that involves neutral time-delay components, the properties of the Lévy process, as well as various inequality approaches, some sufficient exponential stability criteria in non-Lipschitz cases are obtained. Besides, the achieved results depend on the time-delay, noise intensity, and impulse factor. At the end of the paper, two numerical examples with simulations are presented to demonstrate the effectiveness and feasibility of the addressed results

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Stability analysis of hybrid stochastic delayed Cohen-Grossberg neural networks with Lévy noise and Markov switching

Cited by 7 publications

References 30 publications

Laplace transform and nonlinear control design for quasi‐projective synchronization for Caputo inertial delayed neural networks

Laplace transform and nonlinear control design for quasi‐projective synchronization for Caputo inertial delayed neural networks

Delay-Independent Stability of Stochastic Systems with Time-Varying Delay and Lévy Noise

Exponential Stability of Impulsive Stochastic Neutral Neural Networks with Lévy Noise Under Non-Lipschitz Conditions

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