Global Mittag-Leffler stability analysis of impulsive fractional-order complex-valued BAM neural networks with time varying delays

Ali, M. Syed; Narayanan, G.; Shekher, Vineet; Alsaedi, Ahmed; Ahmad, Bashir

doi:10.1016/j.cnsns.2019.105088

Cited by 83 publications

(35 citation statements)

References 50 publications

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“…12+|y| and f (t, y t ), φ(t) will be fixed later. Using the given data, we find that |Ω| ≈ 0.0366186289, Λ 1 ≈ 21.13605055, Λ 2 ≈ 85.89633432, Λ 3 ≈ 3.77976315, Λ 4 ≈ 14.81704598, and Λ 5 = 1.878052710, where Ω, Λ 1 , Λ 2 , Λ 3 , and Λ 4 are given by Equation (6) and Equations (16)- (20) respectively.…”

Section: Examplesmentioning

confidence: 88%

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Nonlinear Impulsive Multi-Order Caputo-Type Generalized Fractional Differential Equations with Infinite Delay

et al. 2019

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We establish sufficient conditions for the existence of solutions for a nonlinear impulsive multi-order Caputo-type generalized fractional differential equation with infinite delay and nonlocal generalized integro-initial value conditions. The existence result is proved by means of Krasnoselskii’s fixed point theorem, while the contraction mapping principle is employed to obtain the uniqueness of solutions for the problem at hand. The paper concludes with illustrative examples.

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Section: Examplesmentioning

confidence: 88%

“…Impulsive fractional differential equation is found to serve in a number of practical applications, for example, fractal porous media [1,2], fractal petroleum [3,4], neural networks [5,6], and physiology [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Impulsive Multi-Order Caputo-Type Generalized Fractional Differential Equations with Infinite Delay

et al. 2019

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“…Figure 1 shows the phase diagram of the drive-response (30) without the controller, indicating that the drive-response synchronization has not been reached yet. Figures 2-5 show the synchronizing behaviors of the drive-response system (30). Compared Figure 1 and Figures 2-5, we can see that the drive-response system (30) reaches synchronization before a fixed point of time T max = 0.069624s.…”

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confidence: 89%

“…Example 2: Consider 3-dimensional FCNNs as the drive-response system without delay items. The parameters and initial values of this system are identical with those of system (30). We design the controller u i (t) as follows.…”

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confidence: 99%

Fixed-Time Synchronization of Fuzzy Cellular Neural Networks With Time-Varying Delays and Discontinuous Activations

Liu

Sun

2020

IEEE Access

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The present paper investigates the fixed-time synchronization for fuzzy cellular neural networks with time-varying delays and discontinuous activations. In the framework of differential inclusions, new and useful fixed-time synchronization criteria for the networks considered are established by utilizing the discontinuous state feedback control and constructing Lyapunov functionals, which significantly generalize and improve recent works in the literature. Numerical simulations are given to show the effectiveness of the fixed-time synchronization schemes. INDEX TERMS Delayed fuzzy cellular neural networks, discontinuous activations, state feedback control, fixed-time synchronization.

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“…Thus, fractional-order artificial neural networks were developed in [1]. Since then, many properties of this type of networks were studied: asymptotic stability and synchronization [2][3][4][5][6][7], Mittag-Leffler stability and synchronization [8][9][10][11][12][13], dissipativity [14][15][16], etc.…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays

Popa

Kaslik

2020

Mathematics

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This paper studies fractional-order neural networks with neutral-type delay, leakage delay, and time-varying delays. A sufficient condition which ensures the finite-time synchronization of these networks based on a state feedback control scheme is deduced using the generalized Gronwall–Bellman inequality. Then, a different state feedback control scheme is employed to realize the finite-time Mittag–Leffler synchronization of these networks by using the fractional-order extension of the Lyapunov direct method for Mittag–Leffler stability. Two numerical examples illustrate the feasibility and the effectiveness of the deduced sufficient criteria.

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Global Mittag-Leffler stability analysis of impulsive fractional-order complex-valued BAM neural networks with time varying delays

Cited by 83 publications

References 50 publications

Nonlinear Impulsive Multi-Order Caputo-Type Generalized Fractional Differential Equations with Infinite Delay

Nonlinear Impulsive Multi-Order Caputo-Type Generalized Fractional Differential Equations with Infinite Delay

Fixed-Time Synchronization of Fuzzy Cellular Neural Networks With Time-Varying Delays and Discontinuous Activations

Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays

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