IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v205y2023icp62-77.html
   My bibliography  Save this article

Synchronization analysis of fractional-order inertial-type neural networks with time delays

Author

Listed:
  • Peng, Qiu
  • Jian, Jigui

Abstract

This paper is dedicated to the global Mittag-Leffler synchronization (GMLS) of fractional-order inertial-type neural networks (FOITNNs) with time delays. To begin with, based on the semigroup property of the Caputo fractional derivative (CFD), an appropriate variable substitution is chosen to transform the original fractional-order inertial system into a traditional fractional-order system. Secondly, two types of discontinuous control schemes with delays and only a control input are proposed: one is the state feedback control and the other is the fractional-order adaptive control. On the basis of Lyapunov stability theory and fractional-order differential inequalities, some new sufficient criteria for the GMLS of two FOITNNs are established. Furthermore, the control gains here can be selected more widely, which makes the results more applicative and less conservative. Finally, two numerical examples validate the efficacy of the obtained results.

Suggested Citation

  • Peng, Qiu & Jian, Jigui, 2023. "Synchronization analysis of fractional-order inertial-type neural networks with time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 62-77.
    • Handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:62-77
    DOI: 10.1016/j.matcom.2022.09.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422004001
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.09.023?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Pratap, A. & Raja, R. & Cao, J. & Lim, C.P. & Bagdasar, O., 2019. "Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 241-260.
    2. Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun & Huang, Junjian, 2018. "Synchronization of fractional-order memristor-based complex-valued neural networks with uncertain parameters and time delays," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 105-123.
    3. Laskin, Nick, 2000. "Fractional market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 482-492.
    4. Grienggrai Rajchakit & Anbalagan Pratap & Ramachandran Raja & Jinde Cao & Jehad Alzabut & Chuangxia Huang, 2019. "Hybrid Control Scheme for Projective Lag Synchronization of Riemann–Liouville Sense Fractional Order Memristive BAM NeuralNetworks with Mixed Delays," Mathematics, MDPI, vol. 7(8), pages 1-23, August.
    5. Zhang, Weiwei & Zhang, Hai & Cao, Jinde & Zhang, Hongmei & Chen, Dingyuan, 2020. "Synchronization of delayed fractional-order complex-valued neural networks with leakage delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    6. Mahmoud, Emad E. & Trikha, Pushali & Jahanzaib, Lone Seth & Almaghrabi, Omar A., 2020. "Dynamical analysis and chaos control of the fractional chaotic ecological model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    7. Tang, Qian & Jian, Jigui, 2019. "Global exponential convergence for impulsive inertial complex-valued neural networks with time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 159(C), pages 39-56.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Luo, Lingao & Li, Lulu & Huang, Wei, 2024. "Asymptotic stability of fractional-order Hopfield neural networks with event-triggered delayed impulses and switching effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 491-504.
    2. Hongguang Fan & Yue Rao & Kaibo Shi & Hui Wen, 2023. "Global Synchronization of Fractional-Order Multi-Delay Coupled Neural Networks with Multi-Link Complicated Structures via Hybrid Impulsive Control," Mathematics, MDPI, vol. 11(14), pages 1-17, July.
    3. Peng, Qiu & Jian, Jigui, 2023. "Asymptotic synchronization of second-fractional -order fuzzy neural networks with impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    4. Wang, Shasha & Jian, Jigui, 2023. "Predefined-time synchronization of incommensurate fractional-order competitive neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    5. Li, Xuemei & Liu, Xinge & Wang, Fengxian, 2023. "Anti-synchronization of fractional-order complex-valued neural networks with a leakage delay and time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Iswarya, M. & Raja, R. & Cao, J. & Niezabitowski, M. & Alzabut, J. & Maharajan, C., 2022. "New results on exponential input-to-state stability analysis of memristor based complex-valued inertial neural networks with proportional and distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 440-461.
    2. Pratap, A. & Raja, R. & Cao, J. & Lim, C.P. & Bagdasar, O., 2019. "Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 241-260.
    3. Wang, Chen & Zhang, Hai & Ye, Renyu & Zhang, Weiwei & Zhang, Hongmei, 2023. "Finite time passivity analysis for Caputo fractional BAM reaction–diffusion delayed neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 424-443.
    4. Jian, Jigui & Wu, Kai & Wang, Baoxian, 2020. "Global Mittag-Leffler boundedness and synchronization for fractional-order chaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    5. Mao, Kun & Liu, Xiaoyang & Cao, Jinde & Hu, Yuanfa, 2022. "Finite-time bipartite synchronization of coupled neural networks with uncertain parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    6. Yi Chen & Jing Dong & Hao Ni, 2021. "ɛ-Strong Simulation of Fractional Brownian Motion and Related Stochastic Differential Equations," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 559-594, May.
    7. Feng, Liang & Hu, Cheng & Yu, Juan & Jiang, Haijun & Wen, Shiping, 2021. "Fixed-time Synchronization of Coupled Memristive Complex-valued Neural Networks," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    8. Ge, Zheng-Ming & Yi, Chang-Xian, 2007. "Chaos in a nonlinear damped Mathieu system, in a nano resonator system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 42-61.
    9. Duan, Lian & Shi, Min & Huang, Chuangxia & Fang, Xianwen, 2021. "Synchronization in finite-/fixed-time of delayed diffusive complex-valued neural networks with discontinuous activations," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    10. Han, Siyu & Hu, Cheng & Yu, Juan & Jiang, Haijun & Wen, Shiping, 2021. "Stabilization of inertial Cohen-Grossberg neural networks with generalized delays: A direct analysis approach," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    11. Tam, Lap Mou & Si Tou, Wai Meng, 2008. "Parametric study of the fractional-order Chen–Lee system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 817-826.
    12. Wang, Fei & Yang, Yongqing & Hu, Manfeng & Xu, Xianyun, 2015. "Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 134-143.
    13. G. Fern'andez-Anaya & L. A. Quezada-T'ellez & B. Nu~nez-Zavala & D. Brun-Battistini, 2019. "Katugampola Generalized Conformal Derivative Approach to Inada Conditions and Solow-Swan Economic Growth Model," Papers 1907.00130, arXiv.org.
    14. Lu, Jun Guo & Chen, Guanrong, 2006. "A note on the fractional-order Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 685-688.
    15. Chen, Dazhao & Zhang, Zhengqiu, 2022. "Globally asymptotic synchronization for complex-valued BAM neural networks by the differential inequality way," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    16. Sheu, Long-Jye & Chen, Hsien-Keng & Chen, Juhn-Horng & Tam, Lap-Mou & Chen, Wen-Chin & Lin, Kuang-Tai & Kang, Yuan, 2008. "Chaos in the Newton–Leipnik system with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 98-103.
    17. Zhang, Hai & Chen, Xinbin & Ye, Renyu & Stamova, Ivanka & Cao, Jinde, 2023. "Adaptive quasi-synchronization analysis for Caputo delayed Cohen–Grossberg neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 49-65.
    18. Wang, Pengfei & Li, Shaoyu & Su, Huan, 2020. "Stabilization of complex-valued stochastic functional differential systems on networks via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    19. Laskin, Nick, 2018. "Valuing options in shot noise market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 518-533.
    20. Ali Balcı, Mehmet, 2017. "Time fractional capital-induced labor migration model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 91-98.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:62-77. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.