Novel results on bifurcation for a fractional-order complex-valued neural network with leakage delay

Yuan, Jialei; Zhao, Lingzhi; Huang, Chengdai; Xiao, Min

doi:10.1016/j.physa.2018.09.138

Cited by 28 publications

(8 citation statements)

References 23 publications

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“…Caputo derivative [38] Hopfield FANN [16,63] Memristive FANN [15] Nonidentical FANN [64] Quaternion-valued FANN [65] Quaternion-valued memristive FANN [41,66] Recurrent FANN FDE [67] Laplace transform method Backpropagation ANN Riemann-Liouville derivative FDE [68] Laplace transform method ANN Grünwald-Letnikov FANN FDE [44] Variational iteration method Feed-forward ANN Riemann-Liouville and Caputo derivative [73] Delayed cellular ANN [74][75][76] Delayed FANN [77,78] Delayed BAM FANN [79][80][81] Delayed complex-valued FANN Delayed FDE [82] Adams-Bashforth-Moulton method Delayed Fuzzy Cellular FANN Caputo derivative [83][84][85][86][87][88][89] Delayed Hopfield FANN [90][91][92] Delayed memristive FANN [93] Delayed memristive quaternion-valued FANN [94] Delayed quaternion-valued FANN Delayed FDE [95] Adams-Bashforth-Moulton method Delayed FANN Riemann-Liouville derivative [96] Delayed competitive FANN Hopfield FANN [74,[100][101][102] Delayed FANN [103][104][105] Delayed BAM FANN…”

Section: Homotopy Perturbation Methodsmentioning

confidence: 99%

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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.

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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.

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Section: Homotopy Perturbation Methodsmentioning

confidence: 99%

“…Delayed Cohen-Grossberg FANN [81,[108][109][110][111][112] Delayed complex-valued FANN [23] Delayed complex-valued BAM FANN [80,113] Delayed complex-valued Hopfield FANN [2] Delayed complex-valued memristive FANN…”

Section: Homotopy Perturbation Methodsmentioning

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.

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“…The "impact of leakage delay on bifurcation in high-order fractional-order BAM neural networks" was researched in [42]. "Novel results on bifurcation for fractional-order complex-valued neural networks with leakage delay" were established in [43]. Lastly, the "dynamic stability of stochastic delayed fractional-order memristor-based fuzzy BAM neural networks with leakage delay" was studied in [44].…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays

Popa

Kaslik

2020

Mathematics

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This paper studies fractional-order neural networks with neutral-type delay, leakage delay, and time-varying delays. A sufficient condition which ensures the finite-time synchronization of these networks based on a state feedback control scheme is deduced using the generalized Gronwall–Bellman inequality. Then, a different state feedback control scheme is employed to realize the finite-time Mittag–Leffler synchronization of these networks by using the fractional-order extension of the Lyapunov direct method for Mittag–Leffler stability. Two numerical examples illustrate the feasibility and the effectiveness of the deduced sufficient criteria.

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“…For example, Eshaghi et al [32] discussed the Hopf bifurcation, chaos control, and synchronization for a chaotic fractionalorder model. Yuan et al [33] obtained the new results on bifurcation for fractional-order complex-valued delayed neural networks. Xiao et al [34] dealt with the fractionalorder PD control of Hopf bifurcations for delayed fractionalorder small-world networks.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Study on Fractional-Order Cohen–Grossberg Neural Networks Involving Delays

Tang

2020

Mathematical Problems in Engineering

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This work is chiefly concerned with the stability behavior and the appearance of Hopf bifurcation of fractional-order delayed Cohen–Grossberg neural networks. Firstly, we study the stability and the appearance of Hopf bifurcation of the involved neural networks with identical delay ϑ 1 = ϑ 2 = ϑ . Secondly, the sufficient criterion to guarantee the stability and the emergence of Hopf bifurcation for given neural networks with the delay ϑ 2 = 0 is set up. Thirdly, we derive the sufficient condition ensuring the stability and the appearance of Hopf bifurcation for given neural networks with the delay ϑ 1 = 0 . The investigation manifests that the delay plays a momentous role in stabilizing networks and controlling the Hopf bifurcation of the addressed fractional-order delayed neural networks. At last, software simulation results successfully verified the rationality of the analytical results. The theoretical findings of this work can be applied to design, control, and optimize neural networks.

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Novel results on bifurcation for a fractional-order complex-valued neural network with leakage delay

Cited by 28 publications

References 23 publications

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

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

Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays

Bifurcation Study on Fractional-Order Cohen–Grossberg Neural Networks Involving Delays

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