Stability analysis of Riemann-Liouville fractional-order neural networks with reaction-diffusion terms and mixed time-varying delays

Wu, Xiang; Liu, Shutang; Wang, Yin

doi:10.1016/j.neucom.2020.12.053

Cited by 33 publications

(12 citation statements)

References 44 publications

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“…Remark 4. In the past, the synchronization of RDNNs and RDCVNNs was usually demonstrated by combining algebraic condition and Lyapunov methods (see [2], [17]- [21], [49], [50]). Theorem 1 and Theorem 2 above does not construct any algebraic condition, different from (see [2],…”

Section: B Synchronization Mechanism With Hybrid Impulsive Actuator S...mentioning

confidence: 99%

“…Recently, a fractional calculus [13], [14] has been actively applied in investigations of networking technologies [15], [16]. In order to describe physical phenomena more accurately, synchronization of fractional-order RDNNs are recognized as a significant im-provement over the integer-order NNs because of their longterm memory and hereditary properties [17]- [21].…”

Section: Introductionmentioning

confidence: 99%

“…[17] Let Ω be cube |w η | < ζ η (η = 1, 2, ..., ) and ϑ(w) = ϑ(w 1 , w 2 , ..., w m ) be a real-valued function which defines on ϑ(w) ∈ C 1 (Ω) and it vanishes on the boundary ∂Ω of Ω, i.e., ϑ(w)| w∈∂Ω = 0. Then Ω ϑ 2 (w)dw ≤ ζ 2…”

mentioning

confidence: 99%

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

et al. 2022

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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.

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Section: B Synchronization Mechanism With Hybrid Impulsive Actuator S...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2022

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“…In recent years, fractional-order systems have become the focus of research, and articles [18][19][20][21] provide stability analysis of Riemann-Liouville neural networks. In the article, 22 the finite-time stability analysis of fractional-order amnestic fuzzy cell neural networks (MFFCNNs) with time delays and leakage terms was studied by using generalized Bernoulli's inequality and Holder's inequality.…”

Section: Introductionmentioning

confidence: 99%

Convergence analysis of Riemann‐Liouville fractional neural network

Dong

Liao

et al. 2022

Math Methods in App Sciences

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Many fractional order calculus researchers believe that fractional order calculus is a good way to solve information processing as well as certain physical system modeling problems. In the training of neural networks, there is the problem of long convergence time. In order to shorten the convergence time of the network, an R-L gradient descent method is proposed in this study. The article begins with a theoretical proof of the convergence of fractional order derivatives using function approximation and interpolation inequality theorems. Finally, through multiple simulations, it can be obtained that the fractional-order neural network can maintain a higher accuracy rate compared with the integer-order neural network, and also can well solve the problem of longer convergence time of the neural network. The convergence time can be reduced by nearly 10% compared to the integer order.

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“…In recent years, many efforts have been dedicated to investigating synchronization of RDNNs with time delays [34]- [36]. Also, relatively recently, reaction-diffusion terms have been incorporated into some fractional-order models [37], [38]. For example, Stamova and Stamov [39] developed impulsive control on Mittag-Leffler synchronization of FONNs with time-varying delays and reaction-diffusion terms.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Fuzzy Feedback Controller Design for Finite-Time Mittag-Leffler Synchronization of Fractional-Order Quaternion-Valued Reaction-Diffusion Fuzzy Molecular Modeling of Delayed Neural Networks

et al. 2021

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This paper addresses an adaptive fuzzy feedback controller design problem for finite-time Mittag-Leffler synchronization (FTMLS) of fractional-order quaternion-valued reaction-diffusion T-S fuzzy molecular modeling of delayed neural networks. A novel approach is proposed to effectively deal with the joint effects from fuzzy rules and reaction-diffusion terms for the class of T-S fuzzy fractional-order reaction-diffusion delayed quaternion-valued neural networks (FORDDQVNNs) under consideration. By employing Lyapunov stability theory, Caputo fractional derivative, several algebraic criteria are established to guarantee the FTMLS of T-S fuzzy FORDDQVNNs via designed fuzzy feedback controller. Moreover, the adaptive controller and parameter update laws are designed via adaptive control methods. Compared with existing results in the literature, we also show that our results are less conservative than existing ones with these illustrative T-S fuzzy FORDDQVNNs. A numerical example is presented to verify the analysis results and illustrate the effectiveness of the proposed FTMLS conditions.INDEX TERMS Quaternion-valued neural networks (QVNNs), Fractional derivatives, Reaction-diffusion terms, Takagi-Sugeno fuzzy, Adaptive control law.

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Stability analysis of Riemann-Liouville fractional-order neural networks with reaction-diffusion terms and mixed time-varying delays

Cited by 33 publications

References 44 publications

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

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

Convergence analysis of Riemann‐Liouville fractional neural network

Adaptive Fuzzy Feedback Controller Design for Finite-Time Mittag-Leffler Synchronization of Fractional-Order Quaternion-Valued Reaction-Diffusion Fuzzy Molecular Modeling of Delayed Neural Networks

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