Stability Analysis for a Class of Impulsive Bidirectional Associative Memory (BAM) Neural Networks with Distributed Delays and Leakage Time-Varying Delays

Aouiti, Chaouki; Assali, El Abed

doi:10.1007/s11063-018-9937-y

Cited by 32 publications

(14 citation statements)

References 39 publications

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“…where (0, 0, 0, 0) = (0, 0, 0, 0) = 0. Suppose that there exist nonnegative constants , , , and such that inequalities (5) and (7) hold:…”

Section: )mentioning

confidence: 99%

“…There will be a distribution of conduction velocities along these pathways and a distribution of propagation be designed with discrete delays. Therefore, the more appropriate way is to incorporate continuously distributed delays [3][4][5][6][7]. In [8][9][10][11], the authors have studied several kinds of complex-valued neural networks with continuously distributed delays.…”

Section: Introductionmentioning

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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“…where (0, 0, 0, 0) = (0, 0, 0, 0) = 0. Suppose that there exist nonnegative constants , , , and such that inequalities (5) and (7) hold:…”

Section: )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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“…Time-varying delays, constant delays, distributed delays are often involved in the study of neural networks. [23][24][25] Motivated by the above discussions, we study the periodic dynamics of MAMNNs with mixed time-varying delays and discontinuous activation functions.…”

Section: Introductionmentioning

confidence: 99%

Periodic dynamics of multidirectional associative neural networks with discontinuous activation functions and mixed time delays

Yan

Qiao

Duan

et al. 2021

Intl J Robust & Nonlinear

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Multidirectional associative memory neural networks (MAMNNs) are constructed to simulate the many-to-many association, and they are applied widely in many fields. It is important to explore the global stability of the periodic solution of MAMNNs. In this paper, MAMNNs with discontinuous activation functions and mixed time-varying delays are considered. Firstly, we investigate the conditions for the existence of the periodic solution by using the Mawhin-like coincidence theorem, and a special connecting weight matrix is constructed to prove the existence of the periodic solution. Secondly, the uniqueness and global exponential stability of the periodic solution are explored for the non-self-connected system by introducing a Lipschitz-like condition. Finally, numerical simulations are given to illustrate the effectiveness of our main results.

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“…[9][10][11] In particular, delay-dependent stability/passivity conditions were derived for BAM neural networks with interval time-varying delays [12][13][14][15][16] using Lyapunov-Krasovskii functional and linear matrix inequality approach. Synchronization, 17,18 stabilization, 19,20 or impulsive control 21,22 problems have also been investigated for various types of BAM neural networks with delays.…”

Section: Introductionmentioning

confidence: 99%

Exponential stability of positive neural networks in bidirectional associative memory model with delays

Hien

Hai-An

2019

Math Methods in App Sciences

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This paper is concerned with the problem of exponential stability of positive neural networks in bidirectional associative memory (BAM) model with multiple time-varying delays and nonlinear self-excitation rates. On the basis of a systematic approach involving extended comparison techniques via differential inequalities, we first prove the positivity of state trajectories initializing from a positive cone called the admissible set of initial conditions. In combination with the use of Brouwer's fixed point theorem and M-matrix theory, we then derive conditions for the existence and global exponential stability of a unique positive equilibrium of the model. An extension to the case of BAM neural networks with proportional delays is also presented. The effectiveness of the obtained results is illustrated by a numerical example with simulations. KEYWORDS exponential stability, M-matrix, positve BAM neural networks, time-varying delays MSC CLASSIFICATION 34 K20; 34 K45; 92C42

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Stability Analysis for a Class of Impulsive Bidirectional Associative Memory (BAM) Neural Networks with Distributed Delays and Leakage Time-Varying Delays

Cited by 32 publications

References 39 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

Periodic dynamics of multidirectional associative neural networks with discontinuous activation functions and mixed time delays

Exponential stability of positive neural networks in bidirectional associative memory model with delays

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