Global adaptive matrix-projective synchronization of delayed fractional-order competitive neural network with different time scales

He, Jin–Man; Chen, Fangqi; Lei, Tengfei; Bi, Qinsheng

doi:10.1007/s00521-020-04728-7

Cited by 21 publications

(9 citation statements)

References 51 publications

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“…Concluding, the Caputo derivative is the most used fractional derivative for investigating the stability of the ANN involved with FC, followed by the Riemann-Liouville derivative. Nowadays, Caputo and Riemann- Adaptive control [188] ANN Synchronization [156] Chebyshev ANN Synchronization [161] Fuzzy ANN Synchronization [13,160] FANN Global projective synchronization [11,154] FANN Global synchronization [55,155] FANN Synchronization [189] Chaotic FANN Approximation and stability [82] Fuzzy cellular FANN Caputo derivative Global stability and synchronization [159] Memristive FANN Projective synchronization [190] Memristive FANN with leakage delay Synchronization [191] Radial basis function FANN Synchronization [158] Delayed FANN Mixed projective synchronization [192] Delayed BAM FANN Stability and synchronization [157] Delayed fuzzy FANN Projective synchronization [109] Delayed complex-valued FANN Quasi-projective and complete synchronization [193] Delayed competitive FANN Projective Synchronization Adaptive sliding mode control [194] Hopfield FANN Caputo derivative Stability [195] Delayed fuzzy FANN Projective synchronization [52] Deep convolutional ANN Robotic manipulators [196] Deep recurrent ANN Synchronization [165] Radial basis function ANN Stability [197] Radial basis function ANN HIV infection model [198,199] Recurrent ANN Approximation [198] Recurrent ANN Stability Sliding Mode Control [58] FANN Caputo derivative Synchronization [200] Chaotic FANN Syncrhonization [201] Memristive MAM FANN Fixed-time synchronization [15] Nonidentical FANN Projective synchronization [166] Delayed Hopfield FAN...…”

Section: Ann Involved With Fc To Reach Stabilitymentioning

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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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: Ann Involved With Fc To Reach Stabilitymentioning

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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“…First, we extend the traditional projective scaling factor to a time-dependent function matrix and define a generalized synchronization mode, i.e., TFMPS. This synchronization mode can degenerate into matrix projective synchronization (PS) [41], modified PS [38], and anti-synchronization under specific restrictive requirements. The adjustability of fractional orders and the time-varying unpredictability of elements in function matrices can improve the safety of secret communication, providing better application prospects for communication encryption systems.…”

Section: Introductionmentioning

confidence: 99%

Time-Varying Function Matrix Projection Synchronization of Caputo Fractional-Order Uncertain Memristive Neural Networks with Multiple Delays via Mixed Open Loop Feedback Control and Impulsive Control

Fan,

Rao,

Shi

et al. 2024

Fractal Fract

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This paper shows solicitude for the generalized projective synchronization of Caputo fractional-order uncertain memristive neural networks (FOUMNNs) with multiple delays. By extending the constant scale factor to the time-varying function matrix, we establish an extraordinary synchronization mode called time-varying function matrix projection synchronization (TFMPS), which is a generalized version of traditional matrix projection synchronization, modified projection synchronization, complete synchronization, and anti-synchronization. To achieve the goal of TFMPS, we design a novel mixed controller including the open loop feedback control and impulsive control, which employs the state information in the time-delayed interval and the sampling information at the impulse instants. It has a prominent advantage that impulse intervals are not restricted by time delays. To establish the connection between the error system and the auxiliary system, a generalized fractional-order comparison theorem with time-varying coefficients and impulses is established. Applying the stability theory, the comparison theorem, and the Laplace transform, new synchronization criteria of FOUMNNs are acquired under the mixed impulsive control schemes, and the derived synchronization theorem and corollary can effectively expand the correlative synchronization achievements of fractional-order systems.

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“…Thus STM means rapid neural activity, while LTM represents the unsupervised slow activity of synaptic modifications induced by inputs. For the past few years, many researchers have investigated the problems of synchronization and stability of CNNs, as well as other dynamical behaviors, please see papers [14][15][16][17][18][19][20] for more information.…”

Section: Introductionmentioning

confidence: 99%

“…[25][26][27][28] Notably, nonlocal CNNs with time lags have played extremely critical roles in science and engineering, which offer the efficient approaches to characterize memory with different scales. 18,19 For instance, by employing the adaptive control method, He et al 18 discussed projection synchronization of nonlocal CNNs with time lags depicted by r c D a 0 P i (t) = Àc i P i (t) +…”

Section: Introductionmentioning

confidence: 99%

Global exponential convergence and synchronization for exponential numerical competitive neural networks with different time scales and fuzzy logic

Yang,

Liu

2024

Proceedings of the Institution of Mechanical Engineers, Part C:

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For nonlocal fuzzy delayed competitive neural networks, a novel difference model is first developed in this article using the Mittag-Leffler Euler difference method. Secondly, the existence of a sole globally bounded solution and globally exponential stability to the discrete-time networks are addressed based on Banach contractive mapping principle and the constant variation formula for sequences. Besides, exponential synchronization of the discrete-time networks is investigated and a feedback controller is designed from the viewpoint of the theory of controls. It is the first time to consider nonlocal fuzzy delayed competitive neural networks by using Mittag-Leffler Euler differences. In contrast to nonlocal discrete approaches, such difference competitive neural networks could preferably figure the features of continuous networks. The difference method in this paper extends and improves the traditional difference approaches, for example, Adams-Bashforth Euler differences. Moreover, this article explores some avenue for the research of discrete-time fractional-order systems and develops a set of theories and methodologies for the future investigations.

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Global adaptive matrix-projective synchronization of delayed fractional-order competitive neural network with different time scales

Cited by 21 publications

References 51 publications

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

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

Time-Varying Function Matrix Projection Synchronization of Caputo Fractional-Order Uncertain Memristive Neural Networks with Multiple Delays via Mixed Open Loop Feedback Control and Impulsive Control

Global exponential convergence and synchronization for exponential numerical competitive neural networks with different time scales and fuzzy logic

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