Global exponential stability analysis of discrete-time BAM neural networks with delays: A mathematical induction approach

Cong, Er-yong; Xiao, Han; Zhang, Xian

doi:10.1016/j.neucom.2019.10.089

Cited by 29 publications

(13 citation statements)

References 23 publications

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“…, the delayed discrete-time CGBAMNN (18) becomes the BAMNN in [23]. Therefore, [23,Theorems 2 and 3] are special cases of Propositions 2 and 3, respectively.…”

Section: Methods Comparisonmentioning

confidence: 99%

“…Remark 4: In [23], the authors investigated the global exponential stability for discrete-time BAM neural network with variable delay. When…”

Section: Methods Comparisonmentioning

confidence: 99%

“…Time delay may lead to some complex dynamical behaviors of the whole network, for example, instability, chaos, periodic, and poor performance [4]- [11]. Therefore, it is great important to determine sufficient conditions for the asymptotic or exponential stability of discretetime delayed BAMNNs [12]- [23].…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the previous discussions, in this paper we study the stabilization issue for delayed discretetime CGBAMNNs via state feedback controller. Based on the mathematical induction method proposed in [23], the state feedback controller is designed. We derive several novel global exponential stability criteria for the equilibrium of the resulting close-loop system, which have simple form, and hence they can be easily verified via the standard tool software (e.g., MATLAB).…”

Section: Introductionmentioning

confidence: 99%

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New Stabilization Method for Delayed Discrete-Time Cohen–Grossberg BAM Neural Networks

2020

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This paper deals with the state feedback stabilization problem of delayed discrete-time Cohen-Grossberg BAM neural networks. By the mathematical induction method, stabilizable conditions are derived to ensure that the resulting closed-loop system is globally exponentially stable, and thereby, the desired state feedback controller is designed. These stabilizable conditions are very simple, which can easily verified by using the standard toolbox software (for example, MATLAB). The proposed approach is directly based on the definition of global exponential stability, and does not involve the construction of any Lyapunov-Krasovskii functional. For a special case, it is theoretical proven that the proposed method is superior to an existing one. Moreover, several illustrative examples are given to validate the success of the derived theoretical results. INDEX TERMS Discrete-time Cohen-Grossberg BAM neural network; Stabilization; Global exponential stability.

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“…, the delayed discrete-time CGBAMNN (18) becomes the BAMNN in [23]. Therefore, [23,Theorems 2 and 3] are special cases of Propositions 2 and 3, respectively.…”

Section: Methods Comparisonmentioning

confidence: 99%

“…Remark 4: In [23], the authors investigated the global exponential stability for discrete-time BAM neural network with variable delay. When…”

Section: Methods Comparisonmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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New Stabilization Method for Delayed Discrete-Time Cohen–Grossberg BAM Neural Networks

2020

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“…Owing to the existence of a multitude of parallel paths with axons of different sizes and lengths, neural networks typically have a spatial extent, and therefore a distribution of propagation delays over a time span occurs [19]. Due to the increasing interest in the asymptotic behavior of solutions for designing neural networks, researchers have recently addressed the stability of delayed neural networks (see for instance [5,8,10,12,[16][17][18]20,23,24,38,39] and references therein). In [18,38,39], a set of sufficient conditions based on the system parameters guaranteeing the exponential stability of various retarded BAM neural network models was derived by analytical techniques and Lyapunov functionals.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behavior of a BAM neural network with delays of distributed type

Othmani

Tatar

Khemmoudj

2021

Math. Model. Nat. Phenom.

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In this paper, we examine a Bidirectional Associative Memory neural network model with distributed delays. Using a result due to Cid [J. Math. Anal. Appl. 281 (2003) 264–275], we were able to prove an exponential stability result in the case when the standard Lipschitz continuity condition is violated. Indeed, we deal with activation functions which may not be Lipschitz continuous. Therefore, the standard Halanay inequality is not applicable. We will use a nonlinear version of this inequality. At the end, the obtained differential inequality which should imply the exponential stability appears ‘state dependent’. That is the usual constant depends in this case on the state itself. This adds some difficulties which we overcome by a suitable argument.

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Further investigation on bifurcation and their control of fractional‐order bidirectional associative memory neural networks involving four neurons and multiple delays

Zhang

Aouiti

et al. 2021

Math Methods in App Sciences

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This work principally probes into the stability, the existence, and control of Hopf bifurcation of new established fractional‐order delayed bidirectional associative memory (BAM) neural networks with four neurons. Firstly, based on the earlier study, we set up a class of new fractional‐order multiple delayed BAM neural networks with four neurons. Secondly, applying an appropriate variable transformation, we get a new equivalent fractional‐order single delayed BAM neural networks with four neurons. With the aid of the stability theory and bifurcation knowledge of fractional‐order differential dynamical systems, a novel sufficient criterion to guarantee the stability and the appearance of Hopf bifurcation of the addressed fractional‐order delayed BAM neural networks is set up. Thirdly, designing a suitable time‐delayed feedback controller, the stability region and the time of appearance of Hopf bifurcation for the involved neural networks have been adjusted. Finally, two simulation examples are presented to illustrate the rationality of the mathematical derivation results. The study vindicates that the time delay has great effect on the stability, bifurcation, and its control for involved network models. The obtained fruits of this work can be effectively applied to control and design neural networks. Also, some research ideas will play a key role in studying the related fractional‐order dynamical models in actual world.

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Global exponential stability analysis of discrete-time BAM neural networks with delays: A mathematical induction approach

Cited by 29 publications

References 23 publications

New Stabilization Method for Delayed Discrete-Time Cohen–Grossberg BAM Neural Networks

New Stabilization Method for Delayed Discrete-Time Cohen–Grossberg BAM Neural Networks

Asymptotic behavior of a BAM neural network with delays of distributed type

Further investigation on bifurcation and their control of fractional‐order bidirectional associative memory neural networks involving four neurons and multiple delays

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