Finite-time Mittag-Leffler synchronization of fractional-order memristive BAM neural networks with time delays

Xiao, Jianying; Zhong, Shouming; Li, Yongtao; Xu, Fang

doi:10.1016/j.neucom.2016.09.049

Cited by 143 publications

(86 citation statements)

References 48 publications

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“…As revealed in (12) and (31), the impulsive control system integrates the advantages of impulsive control and continuous control. [8] analyze the finite-time synchronization of fractionalorder memristive bidirectional associative memory neural networks. By employing Holder inequality, inequality, and Gronwall-Bellman inequality, Yang et al [9] formulate the quasi-uniform synchronization for fractional-order memristive neural networks.…”

Section: Remarkmentioning

confidence: 99%

“…Fractional calculus has been drawing interest over the last decade due to its many applications [1][2][3][4][5][6][7][8][9][10][11][12]. In mathematics and theoretical physics, fractional calculus is a generalization of integer-order calculus that roots in classical analysis theory.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, as a special case of an online learning situation, synchronization of neurodynamic systems have been found to be useful in characterizing and validating the consistency of cooperation [1,8,9,11,12]. In addition, neural synchronization under setting control rules offers an appealing alternative to neuron architectures and information exchange mechanism during neural mutual learning [16].…”

Section: Introductionmentioning

confidence: 99%

“…As far as we know, there is little study. In addition, Lyapunov method [1,8], Razumikhintype stability theory [9,16], infinitesimal generator on analytic semigroup principle [12], adaptive control [17], and mathematical induction method [18] are not very good at estimating the multisynchronization effect. Therefore, for the 2 Complexity multisynchronization of control systems, there would still be a lot of room left.…”

Section: Introductionmentioning

confidence: 99%

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Multisynchronization for Coupled Multistable Fractional-Order Neural Networks via Impulsive Control

Zhang

2017

Complexity

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We show that every subnetwork of a class of coupled fractional-order neural networks consisting of identical subnetworks can have ( + 1) locally Mittag-Leffler stable equilibria. In addition, we give some algebraic criteria for ascertaining the static multisynchronization of coupled fractional-order neural networks with fixed and switching topologies, respectively. The obtained theoretical results characterize multisynchronization feature for multistable control systems. Two numerical examples are given to verify the superiority of the proposed results.

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Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multisynchronization for Coupled Multistable Fractional-Order Neural Networks via Impulsive Control

Zhang

2017

Complexity

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“…This kind of impulsive behaviors can be modelled by impulsive systems [23,25,29,32,[40][41][42]. On the other hand, bidirectional associative memory (BAM) neural networks attract many studies due to its extensive applications in many fields [22][23][24][25][43][44][45][46]. In [43], Kosko first introduced hybrid BAM neural network models.…”

Section: Introductionmentioning

confidence: 99%

Existence and Globally Asymptotic Stability of Equilibrium Solution for Fractional-Order Hybrid BAM Neural Networks with Distributed Delays and Impulses

Zhang

Cao

et al. 2017

Complexity

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This paper investigates the existence and globally asymptotic stability of equilibrium solution for Riemann-Liouville fractionalorder hybrid BAM neural networks with distributed delays and impulses. The factors of such network systems including the distributed delays, impulsive effects, and two different fractional-order derivatives between the -layer and -layer are taken into account synchronously. Based on the contraction mapping principle, the sufficient conditions are derived to ensure the existence and uniqueness of the equilibrium solution for such network systems. By constructing a novel Lyapunov functional composed of fractional integral and definite integral terms, the globally asymptotic stability criteria of the equilibrium solution are obtained, which are dependent on the order of fractional derivative and network parameters. The advantage of our constructed method is that one may directly calculate integer-order derivative of the Lyapunov functional. A numerical example is also presented to show the validity and feasibility of the theoretical results.

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Mittag‐Leffler state estimator design and synchronization analysis for fractional‐order BAM neural networks with time delays

Anbalagan

Raja

Rajchakit

et al. 2019

Adaptive Control & Signal

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Item Type Article Authors Pratap, A.; Dianavinnarasi, J.; Raja, R.; Rajchakit, G.; Cao, J.; Bagdasar, Ovidiu Citation Rajchakit, G., et al (2019) 'Mittag-Leffler state estimator design and synchronization analysis for fractional order BAM neural networks with time delays'. AbstractThis paper deals with the extended design of Mittag-Leffler state estimator and adaptive synchronization for fractional order BAM neural networks (FBNNs) with time delays. By the aid of Lyapunov direct approach and Razumikhin-type method a suitable fractional order Lyapunov functional is constructed and a new set of novel sufficient condition are derived to estimate the neuron states via available output measurements such that the ensuring estimator error system is globally Mittag-Leffler stable. Then, the adaptive feedback control rule is designed, under which the considered FBNNs can achieve Mittag-Leffler adaptive synchronization by means of some fractional order inequality techniques. Moreover, the adaptive feedback control may be utilized even when there is no ideal information from the system parameters. Finally, two numerical simulations are given to reveal the effectiveness of the theoretical consequences.

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Finite-time Mittag-Leffler synchronization of fractional-order memristive BAM neural networks with time delays

Cited by 143 publications

References 48 publications

Multisynchronization for Coupled Multistable Fractional-Order Neural Networks via Impulsive Control

Multisynchronization for Coupled Multistable Fractional-Order Neural Networks via Impulsive Control

Existence and Globally Asymptotic Stability of Equilibrium Solution for Fractional-Order Hybrid BAM Neural Networks with Distributed Delays and Impulses

Mittag‐Leffler state estimator design and synchronization analysis for fractional‐order BAM neural networks with time delays

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