Stochastic stability of fractional-order Markovian jumping complex-valued neural networks with time-varying delays

Aravind, R. Vijay; Balasubramaniam, P.

doi:10.1016/j.neucom.2021.01.053

Cited by 21 publications

(4 citation statements)

References 54 publications

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“…Here, Ξ1, Remark 6 Conditions ( 22) and ( 23) are used to set a limit to the magnitude of K m . The obtained control gain satisfying condition (21) may be larger than the actual requirement, and hence, we can choose appropriate parameter γ m from ( 22) and ( 23) to add a restriction. Then, the optimal control gain will be obtained.…”

Section: Remarkmentioning

confidence: 99%

“…According to our experience, the synchronization method for integer-order Markovian systems cannot be directly expanded to fractional-order systems, thereby posing difficulties in the synchronization study of Markovian systems with a fractional order. Although a few works [21] [22] examined the synchronization of fractional-order Markovian systems, they neglected the variation of state in space caused by the reaction-diffusion phenomenon. Therefore, it is necessary and of great interest to fill the gap in the research on synchronization of fractional-order MRDNNs.…”

Section: Introductionmentioning

confidence: 99%

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Synchronization of Coupled Fractional-order Reaction–Diffusion Neural Networks under Markovian Switching Topologies via Quantized Control

Liu

Yang

Hao

et al. 2022

Preprint

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In this study, we investigated the synchronization of coupled fractional-order Markovian reaction–diffusion neural networks (MRDNNs) with partly unknown transition rates. The novelty of this study lies in two aspects. First, the Markovian switching model and reaction–diffusion term are incorporated into a fractional order system, which is a difficult and uncommon problem in existing studies. The synchronization problem of fractional-order MRDNNs was solved by introducing a continuous frequency distribution model of a fractional integrator. Second, a new set of sufficient synchronization conditions with low conservativeness was derived. The (extended) Wirtinger inequality and delay-partitioning technologies were used to introduce generous free parameters, thereby effectively increasing the range of solutions. Through quantized control, the channel bandwidth and communication rate were reduced. Furthermore, a simulation was performed to illustrate the validity of the results and demonstrate the influence of fractional order and reaction–diffusion term on the synchronization rate of the system.

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Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Synchronization of Coupled Fractional-order Reaction–Diffusion Neural Networks under Markovian Switching Topologies via Quantized Control

Liu

Yang

Hao

et al. 2022

Preprint

View full text Add to dashboard Cite

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“…To our best known, there is a few of stability results for the Caputo fractionalorder random switching system. The stochastic stability analysis of fractionalorder Markov jump complex-valued neural networks with time-varying delay is studied in [14] and the asymptotic stability of nonlinear neutral Caputo fractionalorder stochastic differential systems with variable delay is analyzed in [15]. However, the stability results of fractional-order random switching systems is still lacking, which is a hot issue in the future.…”

Section: Introductionmentioning

confidence: 99%

Almost sure stability of Caputo Fractional-order Markovian switching nonlinear systems

Wang

Long

et al. 2022

Preprint

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In this paper, we address the almost sure stability problem of Caputo fractional-order Markovian switching nonlinear systems. Firstly, for the globally asymptotic stability almost surely (GAS a.s.) and exponential stability almost surely (ES a.s.) of Caputo fractional-order Markovian switching nonlinear systems (CFMNSs) with the constant lower bound initial time, some sufficient conditions are given by the stochastic Multi-Lyapunov function and probability analysis method. Then, for CFMNSs with the variable lower bound initial time, a resetting CFMNSs model is constructed to update synchronously the lower bound initial time and the corresponding initial state value of the above-mentioned system with the change of switching. After that, for CFMNSs with the variable lower bound initial time under the resetting means, the sufficient conditions of GAS a.s. and ES a.s. are given using the probability analysis method and stochastic Multi-Lyapunov function, respectively. Finally, numerical examples show that our results are effective.

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“…Because there are many potential applications of complexvalued neural networks (CVNNs) [22], [23], there has been increasing interest in research and development related to CVNNs, in which neuron states and connection matrices are defined in the complex number domain. Recently, there are lots of interesting results about CVNNs by separating the system into real and imaginary parts [24]- [27].…”

Section: Introductionmentioning

confidence: 99%

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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Stochastic stability of fractional-order Markovian jumping complex-valued neural networks with time-varying delays

Cited by 21 publications

References 54 publications

Synchronization of Coupled Fractional-order Reaction–Diffusion Neural Networks under Markovian Switching Topologies via Quantized Control

Synchronization of Coupled Fractional-order Reaction–Diffusion Neural Networks under Markovian Switching Topologies via Quantized Control

Almost sure stability of Caputo Fractional-order Markovian switching nonlinear systems

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

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