pth moment exponential stability of memristor Cohen–Grossberg BAM neural networks with time-varying delays and reaction–diffusion

Priya, Bandana; Ali, M. Syed; Thakur, Ganesh Kumar; Sanober, Sumaya; Dhupia, Bhawna

doi:10.1016/j.cjph.2021.06.027

Cited by 8 publications

(4 citation statements)

References 49 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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“…The LKF was also used to solve the stabilization problems for RDSs with time-varying delays [1,6]. As a result, time delays are considered for RDSs [3,26,32,33,47,54].…”

Section: Introductionmentioning

confidence: 99%

Impulsive effects on stabilization of stochastic nonlinear reaction-diffusion systems with time delays and boundary feedback control

Gokulakrishnan¹,

Srinivasan²

2022

J. Math. Computer Sci.

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In this paper, we investigate the stabilization of stochastic nonlinear impulsive reaction-diffusion systems (SNIRDSs) with time delays and boundary feedback control via average impulsive interval approach. Boundary feedback control strategy are designed to stabilization of SNIRDSs. By constructing a Lyapunov-Krasovskii functional (LKF), and using Wirtinger's inequality, Gronwall inequality, average impulsive interval approach, sufficient conditions are derived to guarantee the finite-time stability (FTS) of proposed systems. We investigate the stabilization results by designing the control gain matrices for boundary feedback controller. The criterions are expressed in terms of linear matrix inequalities (LMIs) that can be verified by Matlab LMI toolbox. Finally, numerical example are given to verify the efficiency and superiority of proposed stabilization criterions.

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“…Mainly, semi-linear reaction-diffusion PDEs are commonly used to model a variety of real-world phenomenon such as population dynamics and chemical reactions etc., [31], [40]. Many researchers have focused their attention on reactiondiffusion equations due to their wide range of applications, see [1], [11], [12], [17], [25], [33]. Random noise in dynamical systems is caused by external disruptions, measurement errors, and a lack of knowledge of specific parameters.…”

Section: Introductionmentioning

confidence: 99%

Exponential Stability Analysis of Stochastic Semi-Linear Systems With Lèvy Noise

et al. 2022

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The exponential stability of semi-linear stochastic partial differential equations (SPDEs) involving Lèvy type noise is investigated in this paper. By constructing an appropriate Lyapunov function, a new set of sufficient conditions are established in terms of linear matrix inequalities (LMIs) which ensures the mean-square exponentially stability (MSES) of given system with Neumann boundary conditions. Then the H ∞ performance index is introduced to eliminate the disturbance which occurs in the considered system. The boundary control gain is obtained by solving the LMI conditions using the standard MATLAB software. Finally, a numerical example is provided to demonstrate the usefulness of the proposed methods.

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pth moment exponential stability of memristor Cohen–Grossberg BAM neural networks with time-varying delays and reaction–diffusion

Cited by 8 publications

References 49 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

Impulsive effects on stabilization of stochastic nonlinear reaction-diffusion systems with time delays and boundary feedback control

Exponential Stability Analysis of Stochastic Semi-Linear Systems With Lèvy Noise

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