Finite-Time Stability Criteria for a Class of High-Order Fractional Cohen–Grossberg Neural Networks with Delay

Yang, Zhanying; Zhang, Jie; Hu, Junhao; Mashino, Jun

doi:10.1155/2020/3604738

Cited by 3 publications

(15 citation statements)

References 40 publications

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“…Remark In the existing works, there have been many works [36‐38,51] on the FTS of fractional‐order neural networks. The FTS criteria are obtained by virtue of integer‐order Gronwall inequality.…”

Section: Resultsmentioning

confidence: 99%

“…Example Consider the same FOCGNNs appeared in Yang et al [51]

\begin{matrix} alignleft \\ align-1^{c} D_{0}^{℘} x_{i} (κ) = & align-2 - f_{i} (x_{i} (κ)) (g_{i} (x_{i} (κ)) - \sum_{j = 1}^{3} a_{i j} p_{j} (x_{j} (κ)) \\ align-1 & align-2 - \sum_{j = 1}^{3} b_{i j} q_{j} (x_{j} (κ - τ)) - J_{i}), i \in ℕ_{1}^{3}, \end{matrix}

where

A = {false(a_{i j} false)}_{3 \times 3} = ((), \begin{matrix} left left left \\ array 0.027 & array 0.008 & array 0.029 \\ array 0.018 & array 0.017 & array 0.005 \\ array 0.003 & array 0.029 & array 0.029 \end{matrix}), B = {false(b_{i j} false)}_{3 \times 3}

= ((), \begin{matrix} left left left \\ array 0.029 & array 0.004 & array 0.024 \\ array 0.015 & array 0.013 & array 0.029 \\ array 0.024 & array 0.028 & array 0.02 \end{matrix})

…”

Section: Numerical Examplementioning

confidence: 99%

“…However, all these works are concerned with the fractional‐order 0 < ℘ < 1. There are few works [51] on the FTS of FODCGNNs which are concerned with the fractional‐order 1 < ℘ < 2. In fact, fractional‐order systems with the order 1 < ℘ < 2 have been widely used in physics, mechanics, and information science [51].…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the above discussions, the FTS of FODCGNNs with the order 1 < ℘ < 2 is investigated in this paper. The main contributions are listed in the following aspects: Different from the existing works [51], in which the integer‐order Gronwall inequality with nonlinear term in the integral has been used to investigate the FTS of FODCGNNs, the fractional‐order delayed Gronwall inequality is applied to study the FTS of FODCGNNs with the order 1 < ℘ < 2. The established criterion for the FTS of FODCGNNs with the order 1 < ℘ < 2 is less conservative than the existing one [51]. …”

Section: Introductionmentioning

confidence: 99%

“…The established criterion for the FTS of FODCGNNs with the order 1 < ℘ < 2 is less conservative than the existing one [51].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

New results on finite‐time stability of fractional‐order Cohen–Grossberg neural networks with time delays

2021

Asian Journal of Control

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The finite‐time stability (FTS) of fractional‐order delayed Cohen–Grossberg neural networks (FODCGNNs) with the order ℘ ∈ (1, 2) is investigated in this study. Based on the fractional‐order delayed Gronwall inequality (FODGI), a new sufficient condition to guarantee the FTS of FODCGNNs is established, which reduces the conservation of the existing criterion. Finally, one numerical example is exhibited to illustrate the effectiveness and less conservativeness of the obtained results.

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Section: Resultsmentioning

confidence: 99%

“…Example Consider the same FOCGNNs appeared in Yang et al [51]

\begin{matrix} alignleft \\ align-1^{c} D_{0}^{℘} x_{i} (κ) = & align-2 - f_{i} (x_{i} (κ)) (g_{i} (x_{i} (κ)) - \sum_{j = 1}^{3} a_{i j} p_{j} (x_{j} (κ)) \\ align-1 & align-2 - \sum_{j = 1}^{3} b_{i j} q_{j} (x_{j} (κ - τ)) - J_{i}), i \in ℕ_{1}^{3}, \end{matrix}

where

A = {false(a_{i j} false)}_{3 \times 3} = ((), \begin{matrix} left left left \\ array 0.027 & array 0.008 & array 0.029 \\ array 0.018 & array 0.017 & array 0.005 \\ array 0.003 & array 0.029 & array 0.029 \end{matrix}), B = {false(b_{i j} false)}_{3 \times 3}

= ((), \begin{matrix} left left left \\ array 0.029 & array 0.004 & array 0.024 \\ array 0.015 & array 0.013 & array 0.029 \\ array 0.024 & array 0.028 & array 0.02 \end{matrix})

…”

Section: Numerical Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The established criterion for the FTS of FODCGNNs with the order 1 < ℘ < 2 is less conservative than the existing one [51].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

New results on finite‐time stability of fractional‐order Cohen–Grossberg neural networks with time delays

2021

Asian Journal of Control

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show abstract

Neutral Caputo-Fabrizio Fractional Differential Equation with Hyers-Ulam Stability

Rohman,

Eryılmaz,

Huda

2023

IJMA

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show abstract

Lyapunov Functions and Stability Properties of Fractional Cohen–Grossberg Neural Networks Models with Delays

Agarwal,

Hristova,

O’Regan

2023

Fractal Fract

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Some inequalities for generalized proportional Riemann–Liouville fractional derivatives (RLGFDs) of convex functions are proven. As a special case, inequalities for the RLGFDs of the most-applicable Lyapunov functions such as the ones defined as a quadratic function or the ones defined by absolute values were obtained. These Lyapunov functions were combined with a modification of the Razumikhin method to study the stability properties of the Cohen–Grossberg model of neural networks with both time-variable and continuously distributed delays, time-varying coefficients, and RLGFDs. The initial-value problem was set and studied. Upper bounds by exponential functions of the solutions were obtained on intervals excluding the initial time. The asymptotic behavior of the solutions of the model was studied. Some of the obtained theoretical results were applied to a particular example.

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Finite-Time Stability Criteria for a Class of High-Order Fractional Cohen–Grossberg Neural Networks with Delay

Cited by 3 publications

References 40 publications

New results on finite‐time stability of fractional‐order Cohen–Grossberg neural networks with time delays

New results on finite‐time stability of fractional‐order Cohen–Grossberg neural networks with time delays

Neutral Caputo-Fabrizio Fractional Differential Equation with Hyers-Ulam Stability

Lyapunov Functions and Stability Properties of Fractional Cohen–Grossberg Neural Networks Models with Delays

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