Global Mittag-Leffler stability analysis of fractional-order impulsive neural networks with one-side Lipschitz condition

Zhang, Xinxin; Niu, Peifeng; Ma, Yunpeng; Wei, Yan-Qiao; Li, Guoqiang

doi:10.1016/j.neunet.2017.06.010

Cited by 34 publications

(15 citation statements)

References 39 publications

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“…The designed impulsive fractional-like neural network model generalizes many existing integer-order neural networks [ 1 , 2 , 3 , 4 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 ]. The main advantages of the proposed model are in (i) incorporating of the hereditary and memory characteristics of fractional derivatives [ 26 , 27 , 28 , 29 , 30 ]; (ii) using the computational simplicity of the generalized FLDs and integrals; (iii) taking into account the effects of some impulsive perturbations that can be used as controls of the neural network’s performance.…”

Section: Impulsive Fractional-like Neural Network: Main Notions Amentioning

confidence: 99%

“…Following the theory of impulsive fractional-order neural network systems [ 27 , 30 ], and the new theory of impulsive fractional-like systems [ 51 , 52 , 53 ], the solutions

of the neural network models (1) are piecewise continuous functions that have points of discontinuity of the first kind

and are left continuous at these moments. For such functions, the following identities are satisfied:

…”

Section: Impulsive Fractional-like Neural Network: Main Notions Amentioning

confidence: 99%

“…The notion of exponential stability has been generalized in [ 66 ] to this of Mittag–Leffler stability for fractional-order systems. For Mittag–Leffler stability results of fractional neural networks see, for example [ 27 , 28 , 30 ] and the bibliography therein. With the present research, we will complement the existing results and will present results on

-practical exponential stability for impulsive fractional-like neural network systems.…”

Section: Impulsive Fractional-like Neural Network: Main Notions Amentioning

confidence: 99%

“…Due to the hereditary and memory characteristics of fractional derivatives, many real world processes and phenomena are better described by fractional-order models, such as system identification of thermal dynamics of buildings, entropy and information [ 18 , 19 , 20 , 21 ]. In addition, the dynamics, chaotic behavior, stability and synchronization of numerous fractional-order neural network models have been investigated in the recent literature [ 22 , 23 , 24 , 25 ], including the behavior of fractional impulsive neural networks [ 26 , 27 , 28 , 29 , 30 ]. Besides the most applicable Riemann-Liouville and Caputo types of fractional derivatives, many new types of fractional derivatives were introduced by the researchers.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Design and Practical Stability of a New Class of Impulsive Fractional-Like Neural Networks

Stamov

Stamova

Martynyuk

et al. 2020

Entropy

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In this paper, a new class of impulsive neural networks with fractional-like derivatives is defined, and the practical stability properties of the solutions are investigated. The stability analysis exploits a new type of Lyapunov-like functions and their derivatives. Furthermore, the obtained results are applied to a bidirectional associative memory (BAM) neural network model with fractional-like derivatives. Some new results for the introduced neural network models with uncertain values of the parameters are also obtained.

show abstract

Section: Impulsive Fractional-like Neural Network: Main Notions Amentioning

confidence: 99%

“…Following the theory of impulsive fractional-order neural network systems [ 27 , 30 ], and the new theory of impulsive fractional-like systems [ 51 , 52 , 53 ], the solutions

of the neural network models (1) are piecewise continuous functions that have points of discontinuity of the first kind

and are left continuous at these moments. For such functions, the following identities are satisfied:

…”

Section: Impulsive Fractional-like Neural Network: Main Notions Amentioning

confidence: 99%

-practical exponential stability for impulsive fractional-like neural network systems.…”

Section: Impulsive Fractional-like Neural Network: Main Notions Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Design and Practical Stability of a New Class of Impulsive Fractional-Like Neural Networks

Stamov

Stamova

Martynyuk

et al. 2020

Entropy

View full text Add to dashboard Cite

show abstract

“…See, for example some recent publications [31][32][33][34][35] and the references therein. Some researchers used classical fractional-order models while new fractional differential systems, including impulsive fractional models started to be explored [36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

Impulsive Delayed Lasota–Wazewska Fractional Models: Global Stability of Integral Manifolds

Stamov

Stamova

2019

Mathematics

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In this paper we deal with the problems of existence, boundedness and global stability of integral manifolds for impulsive Lasota–Wazewska equations of fractional order with time-varying delays and variable impulsive perturbations. The main results are obtained by employing the fractional Lyapunov method and comparison principle for impulsive fractional differential equations. With this research we generalize and improve some existing results on fractional-order models of cell production systems. These models and applied technique can be used in the investigation of integral manifolds in a wide range of biological and chemical processes.

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Distributed asynchronous impulsive consensus of one‐sided Lipschitz nonlinear multi‐agent systems

Zhang

Cui

2021

Intl J Robust & Nonlinear

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This article investigates the consensus problem of one‐sided Lipschitz nonlinear multi‐agent systems (MASs) with distributed asynchronous impulsive control protocol. Based on the theory of discontinuous Lyapunov stability and impulsive differential equation, some new sufficient criteria about asynchronous impulsive control are derived to guarantee the consensus of one‐sided Lipschitz nonlinear MASs. Different from the existing methods of synchronous impulsive control, the asynchronous impulsive control does not need all agents are controlled simultaneously at one impulsive instant. Compared with the traditional Lipschitz condition, the one‐sided Lipschitz nonlinear function considered in this article can obtain a wider nonlinear range. Finally, some numerical simulation examples are given to verify the correctness of the theoretical analysis.

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Global Mittag-Leffler stability analysis of fractional-order impulsive neural networks with one-side Lipschitz condition

Cited by 34 publications

References 39 publications

Design and Practical Stability of a New Class of Impulsive Fractional-Like Neural Networks

Design and Practical Stability of a New Class of Impulsive Fractional-Like Neural Networks

Impulsive Delayed Lasota–Wazewska Fractional Models: Global Stability of Integral Manifolds

Distributed asynchronous impulsive consensus of one‐sided Lipschitz nonlinear multi‐agent systems

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