Finite Time Stability Analysis of Fractional-Order Complex-Valued Memristive Neural Networks with Proportional Delays

Ali, M. Syed; Narayanan, G.; Orman, Zeynep; Shekher, Vineet; Arik, Sabri

doi:10.1007/s11063-019-10097-7

Cited by 47 publications

(12 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Adaptive impulsive control Complex-valued FANN Caputo derivative [232] Interval projection FANN [271] Delayed BAM FANN Uniform stability [241] FANN [237] FANN with and without delays [76,242] Delayed FANN [240] Hopfield FANN [239] Memristive FANN [272] Delayed memristive FANN Caputo derivative [273] Delayed memristive fuzzy BAM FANN [238] Cellular FANN [79,233,234] Delayed complex-valued FANN [235,236] Delayed BAM FANN [274] Delayed BAM FANN Finite-time Stability [248] FANN [75,85,246,275] Delayed FANN [247] Delayed FANN [112,243,276] Delayed complex-valued FANN [277] Delayed complex-valued memristive FANN [244] Delayed complex-valued memristive FANN Caputo derivative [175] Cohen-Grossberg memristive FANN [245] Delayed Cohen-Grossberg FANN [89] Delayed Hopfield FANN [207] Delayed BAM FANN [103] Delayed BAM FANN Global stability [28] FANN [59] BAM FANN [278] Delayed BAM FANN [62] Fuzzy FANN [38,256] Hopfield FANN [86] Delayed Hopfield FANN Caputo derivative [16] Memristive FANN…”

Section: Global Synchronizationmentioning

confidence: 99%

Artificial neural networks: a practical review of applications involving fractional calculus

Viera-Martin

Gómez-Aguilar

Solís-Pérez

et al. 2022

Eur. Phys. J. Spec. Top.

View full text Add to dashboard Cite

In this work, a bibliographic analysis on artificial neural networks (ANNs) using fractional calculus (FC) theory has been developed to summarize the main features and applications of the ANNs. ANN is a mathematical modeling tool used in several sciences and engineering fields. FC has been mainly applied on ANNs with three different objectives, such as systems stabilization, systems synchronization, and parameters training, using optimization algorithms. FC and some control strategies have been satisfactorily employed to attain the synchronization and stabilization of ANNs. To show this fact, in this manuscript are summarized, the architecture of the systems, the control strategies, and the fractional derivatives used in each research work, also, the achieved goals are presented. Regarding the parameters training using optimization algorithms issue, in this manuscript, the systems types, the fractional derivatives involved, and the optimization algorithm employed to train the ANN parameters are also presented. In most of the works found in the literature where ANNs and FC are involved, the authors focused on controlling the systems using synchronization and stabilization. Furthermore, recent applications of ANNs with FC in several fields such as medicine, cryptographic, image processing, robotic are reviewed in detail in this manuscript. Works with applications, such as chaos analysis, functions approximation, heat transfer process, periodicity, and dissipativity, also were included. Almost to the end of the paper, several future research topics arising on ANNs involved with FC are recommended to the researchers community. From the bibliographic review, we concluded that the Caputo derivative is the most utilized derivative for solving problems with ANNs because its initial values take the same form as the differential equations of integer-order.

show abstract

Section: Global Synchronizationmentioning

confidence: 99%

Artificial neural networks: a practical review of applications involving fractional calculus

Viera-Martin

Gómez-Aguilar

Solís-Pérez

et al. 2022

Eur. Phys. J. Spec. Top.

View full text Add to dashboard Cite

show abstract

“…Furthermore, to quantitatively show the effectiveness of the encryption algorithm in this article, a table of correlation coefficients of original and encrypted "Lena" is provided, that is Table I. To test the correlation between two adjacent pixels in original and encrypted image, the following procedure was carried out [26]. The correction can be calculated by It can be seen from Table I, that the correlation coefficients of the original grayscale image are very close to 1, and those of the encrypted grayscale image are very close to 0.…”

Section: Chaotic Encryption and Decryption Mechanismmentioning

confidence: 99%

Impulsive Synchronization Control Mechanism for Fractional-Order Complex-Valued Reaction-Diffusion Systems With Sampled-Data Control: Its Application to Image Encryption

et al. 2022

Self Cite

View full text Add to dashboard Cite

This article is devoted to gain a better understanding of the synchronization control mechanism in networked, complex-valued reaction-diffusion systems via an impulsive and sampled-data controller. Different from the traditional control methods with hybrid mechanism, an impulsive and sampled-data control scheme is proposed for fractional-order complex-valued reaction-diffusion neural networks (FRDCVNNs). By utilizing Lyapunov functional and inequality techniques, finite-time Mittag-Leffler synchronization criteria via an impulsive and sampled-data controller are established and presented as linear matrix inequalities (LMIs), which can ensure the finite-time synchronization of error system containing the drive and response dynamics. In addition, synchronization control mechanism on the considered system via impulsive actuator saturation and sampled-data control are applied. Simulation examples are provided to verify the efficacy of the proposed synchronization criterion and the results of practical application to image encryption scheme based on the chaotic complex system is presented. Furthermore, the proposed cryptosystem have obvious advantages of large key space and high security.

show abstract

“…Nowadays, some interesting results on fractional-order complex-valued memristive neural networks (FCVMNNs) have been published. [40][41][42][43][44][45] However, due to the limited switching speed of the amplifier, time delay is unavoidable in neural network circuits, which could influence the stability of the system. [45,46] Taking these facts into consideration, time delay should be considered in the FCVMNNs.…”

Section: Introductionmentioning

confidence: 99%

Finite-time Mittag–Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay

Wang¹,

Ding²,

Li³

et al. 2022

Chinese Phys. B

View full text Add to dashboard Cite

Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks (FCVMNNs) with time delay is investigated. Firstly, based on the complex-valued sign function, a novel complex-valued feedback controller is devised to research such systems. Under the framework of Filippov solution, differential inclusion theory and Lyapunov stability theorem, the finite-time Mittag-Leffler synchronization (FTMLS) of FCVMNNs with time delay can be realized. Meanwhile, the upper bound of the synchronization settling time (SST) is less conservative than previous results. In addition, by adjusting controller parameters, the global asymptotic synchronization of FCVMNNs with time delay can be also realized, which improves and enrich some existing results. At last, some simulation examples are designed to verify the validity of conclusions.

show abstract

Finite Time Stability Analysis of Fractional-Order Complex-Valued Memristive Neural Networks with Proportional Delays

Cited by 47 publications

References 46 publications

Artificial neural networks: a practical review of applications involving fractional calculus

Artificial neural networks: a practical review of applications involving fractional calculus

Impulsive Synchronization Control Mechanism for Fractional-Order Complex-Valued Reaction-Diffusion Systems With Sampled-Data Control: Its Application to Image Encryption

Finite-time Mittag–Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay

Contact Info

Product

Resources

About