The new fractional discrete neural network model under electromagnetic radiation: Chaos, control and synchronization

Heilat, Ahmed Salem; Karoun, Rabia Chaimaà; Al-Husban, Abdallah; Abbes, Abderrahmane; Horani, Mohammed Al; Grassi, Giuseppe; Ouannas, Adel

doi:10.1016/j.aej.2023.06.017

Cited by 5 publications

(8 citation statements)

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“…For a more complete background regarding discrete fractional calculus, the reader is referred to [62,63,65]. For more results regarding discrete fractional-order neural networks, see [23][24][25][26][27][28][29][30].…”

Section: The Proposed Fractional Discrete Calculus Neural Network Mod...mentioning

confidence: 99%

“…At present, there are various control approaches adopted to discrete fractional-order neural network models to ensure the stability, synchronization, quazi-synchronization and stabilization of the states [23][24][25][26][27][28][29][30].…”

Section: Impulsive Controllersmentioning

confidence: 99%

“…In particular, the applicability of fractional discrete neural networks models is motivated from the point of view of computer simulation and the actual applications of neural networks. This explains the growing research activity in the design, research and application of discrete fractional neural networks [23][24][25][26][27][28][29][30]. Despite the many reported results, the topic of using discrete fractional ANNs as a modeling approach in product form design is still unexplored.…”

Section: Introductionmentioning

confidence: 99%

“…Numerous researchers in the industrial design area have studied the importance of different design control strategies [35][36][37]. In particular, nonlinear controllers [23], linear controllers [28,31], feedback controllers [29] and adaptive controllers [30] are widely applied in the reported discrete fractional-order ANN models.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, stability is one of the most important issues if an ANN model is to be used in practical applications [49]. This has motivated numerous studies on the development of stable neural control strategies for different types of ANN models [38,[40][41][42]44,[50][51][52], including fractional-order neural networks of a continuous and discrete nature [23,24,27,28,30,43,46,47]. For discrete fractional-order neural network models, considerable investigations have been devoted to investigating the Mittag-Lefller stability properties [28,30], which generalize the exponential stability ones.…”

Section: Introductionmentioning

confidence: 99%

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Impulsive Control Discrete Fractional Neural Networks in Product Form Design: Practical Mittag-Leffler Stability Criteria

Stamov

2024

Applied Sciences

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The planning, regulation and effectiveness of the product design process depend on various characteristics. Recently, bio-inspired collective intelligence approaches have been applied in this process in order to create more appealing product forms and optimize the design process. In fact, the use of neural network models in product form design analysis is a complex process, in which the type of network has to be determined, as well as the structure of the network layers and the neurons in them; the connection coefficients, inputs and outputs have to be explored; and the data have to be collected. In this paper, an impulsive discrete fractional neural network modeling approach is introduced for product design analysis. The proposed model extends and complements several existing integer-order neural network models to the generalized impulsive discrete fractional-order setting, which is a more flexible mechanism to study product form design. Since control and stability methods are fundamental in the construction and practical significance of a neural network model, appropriate impulsive controllers are designed, and practical Mittag-Leffler stability criteria are proposed. The Lyapunov function strategy is applied in providing the stability criteria and their efficiency is demonstrated via examples and a discussion. The established examples also illustrate the role of impulsive controllers in stabilizing the behavior of the neuronal states. The proposed modeling approach and the stability results are applicable to numerous industrial design tasks in which multi-agent systems are implemented.

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