Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays

Aouiti, Chaouki

doi:10.1007/s11571-016-9405-1

Cited by 61 publications

(7 citation statements)

References 51 publications

(53 reference statements)

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“…Remark 9. By substituting (13) into (14) and considering the computation rule in Lemma 8, we can obtain the following equation, which will be used in the process of the proof for theorems follow-up.…”

Section: )mentioning

confidence: 99%

“…In fact, most real models of neural networks are affected by many external and internal perturbations which are of great uncertainty, such as impulsive disturbances [5,[9][10][11][12][13][14][15], Markovian jumping parameters [16][17][18][19], and parameter uncertainties [20][21][22]. As Haykin [23] points out, in real nervous systems, synaptic transmission is a noisy process brought on by random fluctuations from the release of neurotransmitters and other probabilistic causes.…”

Section: Introductionmentioning

confidence: 99%

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Mean Square Exponential Stability of Stochastic Complex-Valued Neural Networks with Mixed Delays

Yang

2019

Complexity

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This paper investigates the mean square exponential stability problem of a class of complex-valued neural networks with stochastic disturbance and mixed delays including both time-varying delays and continuously distributed delays. Under different assumption conditions concerning stochastic disturbance term from the existing ones, some sufficient conditions are derived for assuring the mean square exponential stability of the equilibrium point of the system based on the vector Lyapunov function method and Ito^ differential-integral theorem. The obtained results not only generalize the existing ones, but also reduce the conservatism of the previous stability results about complex-valued neural networks with stochastic disturbances. Two numerical examples with simulation results are given to verify the feasibility of the proposed results.

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Section: )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mean Square Exponential Stability of Stochastic Complex-Valued Neural Networks with Mixed Delays

Yang

2019

Complexity

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“…In the nervous system, the time-delays occur due to the propagation time of neurotransmitters forming presynaptic neurons to postsynaptic neurons. e time delays are occurring not only in constant manner [14] but also according to the number of parallel pathways with different lengths and sizes of the axon; it may be classified into various kinds such as discrete [15,16], distributed, and mixed delays [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Existence, Uniqueness, and Exponential Stability of Uncertain Delayed Neural Networks with Inertial Term: Nonreduced Order Case

Iswarya

Raja

Zhu

et al. 2021

Mathematical Problems in Engineering

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In this work, we mainly focus on uncertain delayed neural network system with inertial term. Here, the existence, uniqueness, and exponential stability of inertial neural networks are derived without shifting the second order differential system into first order through substituting variables. Initially, we construct a proper Lyapunov–Krasovskii functional to investigate the stability of novel uncertain delayed inertial neural networks, which is different from the classical Lyapunov functional approach. By utilizing the Kirchhoff’s matrix tree theorem, Cauchy–Schwartz inequality, homeomorphism theorem, and some inequality techniques, the necessary and sufficient conditions are derived for the designed framework. Subsequently, to exhibit the strength of this outcome, we framed a quantitative example.

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“…Up to now, there are some excellent results about the synchronization of discontinuous NNs with a different type of delays. [8][9][10] For instance, in Reference 8, the authors pointed out that the global robust stability of delayed interval RNNs which contain time-invariant uncertain parameters, by using Lyapunov function and matrix-norm inequality. In Reference 9, the authors studied the problem of global asymptotical stability for RNNs with both discrete time-varying delays and distributed time-varying delays, by employing the Lyapunov-Krasovskii functional and linear matrix inequality (LMI).…”

Section: Introductionmentioning

confidence: 99%

Finite‐time and fixed‐time synchronization of fuzzy Clifford‐valued Cohen‐Grossberg neural networks with discontinuous activations and time‐varying delays

Aouiti

Bessifi

2021

Adaptive Control & Signal

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In this article, we are concerned with fuzzy Clifford-valued Cohen-Grossberg neural networks (FCVCGNNs) via discontinuous activations and time-varying delays. First, the time-delayed feedback strategy is used to investigate the synchronization in finite-time and fixed-time of FCVCGNNs with discontinuous activations and time-varying delays. By designing Lyapunov functions and utilizing differential inequalities, several effective conditions are derived to ensure synchronization in finite-time and fixed-time of the addressed neural networks. A novel fixed-time convergence method is proposed to study synchronization in fixed-time of discontinuous delayed FCVCGNNs. Furthermore, the settling time of synchronization are estimated. In the end, two numerical examples with simulations are given to confirm the effectiveness of the synchronization criteria.

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Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays

Cited by 61 publications

References 51 publications

Mean Square Exponential Stability of Stochastic Complex-Valued Neural Networks with Mixed Delays

Mean Square Exponential Stability of Stochastic Complex-Valued Neural Networks with Mixed Delays

Existence, Uniqueness, and Exponential Stability of Uncertain Delayed Neural Networks with Inertial Term: Nonreduced Order Case

Finite‐time and fixed‐time synchronization of fuzzy Clifford‐valued Cohen‐Grossberg neural networks with discontinuous activations and time‐varying delays

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