Stability analysis and robust synchronization of fractional‐order competitive neural networks with different time scales and impulsive perturbations

Anbalagan, Pratap; Raja, R.; Agarwal, Ravi P.; Cao, Jinde

doi:10.1002/acs.3056

Cited by 31 publications

(17 citation statements)

References 68 publications

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“…While many useful results have been achieved, one challenge remains, i.e., the unavoidable phenomenon of time delay in NNs. In this regard, poor signal propagation, chaos, low functionality, divergence, and uncertainty are all examples of dynamics caused by time delays [5]- [9]. As such, it is worthwhile to analyze the dynamics of NNs subject to constant or time-varying delays.…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Synchronization of Clifford-Valued Neural Networks With Infinite Distributed Delays and Impulses

et al. 2021

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We study the issue of finite-time synchronization pertaining to a class of Cliffordvalued neural networks with discrete and infinite distributed delays and impulse phenomena. Since multiplication of Clifford numbers is of non-commutativity, we decompose the original n-dimensional Clifford-valued drive and response systems into the equivalent 2 m -dimensional real-valued counterparts. We then derive the finite-time synchronization criteria concerning the decomposed real-valued drive and response models through new Lyapunov-Krasovskii functional and suitable controller as well as new computational techniques. We also demonstrate the usefulness of the results through a simulation example.INDEX TERMS Clifford-valued neural networks, finite-time synchronization, infinite distributed delay, Lyapunov-Krasovskii fractional.

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Section: Introductionmentioning

confidence: 99%

Finite-Time Synchronization of Clifford-Valued Neural Networks With Infinite Distributed Delays and Impulses

et al. 2021

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“…Finally, fractional power series ANN for solving: delay fractional optimal control problems and fractional optimal control problems with equality and inequal- [224] Competitive FANN Robust synchronization and stability [114] Delayed Competitive FANN Global asymptotic stability [101] Delayed FANN…”

Section: Ann Involved With Fc: Applications In Approximation Of Funct...mentioning

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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“…For a given period of time, the limited distributed delay should be used to compare the current behavior of the state with the distant past, which has less impact. For example, many research works are related to the stability of mixed delay [13,27].…”

Section: Introductionmentioning

confidence: 99%

A Lyapunov–Krasovskii Functional Approach to Stability and Linear Feedback Synchronization Control for Nonlinear Multi-Agent Systems with Mixed Time Delays

Stephen

Raja

Alzabut

et al. 2021

Mathematical Problems in Engineering

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This study focuses on mixed time delayed, both leaderless and leader-follower problems of nonlinear multi-agent systems. Here, we find the stability criteria for multi-agent systems (MASs) by utilizing a proposed lemma, the Lyapunov–Krasovskii functions, analytical techniques, Kronecker product, and some general specifications to obtain the asymptotic stability for the constructed MASs. Furthermore, the criteria to establish the synchronization of leader-follower multiagent systems with linear feedback controllers are discussed. Finally, we provide two numerical calculations along with the computational simulations to check the validity of the theoretical findings reported for both leaderless and leader-follower problem in this study.

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Stability analysis and robust synchronization of fractional‐order competitive neural networks with different time scales and impulsive perturbations

Cited by 31 publications

References 68 publications

Finite-Time Synchronization of Clifford-Valued Neural Networks With Infinite Distributed Delays and Impulses

Finite-Time Synchronization of Clifford-Valued Neural Networks With Infinite Distributed Delays and Impulses

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

A Lyapunov–Krasovskii Functional Approach to Stability and Linear Feedback Synchronization Control for Nonlinear Multi-Agent Systems with Mixed Time Delays

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