IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i24p4823-d1007796.html
   My bibliography  Save this article

Stability and Synchronization of Fractional-Order Complex-Valued Inertial Neural Networks: A Direct Approach

Author

Listed:
  • Hualin Song

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China)

  • Cheng Hu

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China)

  • Juan Yu

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China)

Abstract

This paper is dedicated to the asymptotic stability and synchronization for a type of fractional complex-valued inertial neural network by developing a direct analysis method. First, a new fractional differential inequality is presented for nonnegative functions, which provides an effective tool for the convergence analysis of fractional-order systems. Moreover, instead of the previous separation analysis for complex-valued neural networks, a class of Lyapunov functions composed of the complex-valued states and their fractional derivatives is constructed, and some compact stability criteria are derived. In synchronization analysis, unlike the existing control schemes for reduced-order subsystems, some feedback and adaptive control schemes, formed by the linear part and the fractional derivative part, are directly designed for the response fractional inertial neural networks, and some synchronization conditions are derived using the established fractional inequality. Finally, the theoretical analysis is supported via two numerical examples.

Suggested Citation

  • Hualin Song & Cheng Hu & Juan Yu, 2022. "Stability and Synchronization of Fractional-Order Complex-Valued Inertial Neural Networks: A Direct Approach," Mathematics, MDPI, vol. 10(24), pages 1-23, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4823-:d:1007796
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/24/4823/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/24/4823/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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).
    2. Yaning Yu & Ziye Zhang, 2022. "State Estimation for Complex-Valued Inertial Neural Networks with Multiple Time Delays," Mathematics, MDPI, vol. 10(10), pages 1-14, May.
    3. Bai, Zhenguo & Yang, Tianhui, 2022. "Spreading speeds of cellular neural networks model with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    4. Ravi Agarwal & Snezhana Hristova, 2022. "Impulsive Memristive Cohen–Grossberg Neural Networks Modeled by Short Term Generalized Proportional Caputo Fractional Derivative and Synchronization Analysis," Mathematics, MDPI, vol. 10(13), pages 1-12, July.
    5. Marat Akhmet & Madina Tleubergenova & Akylbek Zhamanshin, 2020. "Inertial Neural Networks with Unpredictable Oscillations," Mathematics, MDPI, vol. 8(10), pages 1-11, October.
    6. Wei, Xiaofeng & Zhang, Ziye & Lin, Chong & Chen, Jian, 2021. "Synchronization and anti-synchronization for complex-valued inertial neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    7. Rathinasamy, Anandaraman & Mayavel, Pichamuthu, 2023. "Strong convergence and almost sure exponential stability of balanced numerical approximations to stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    8. Mohammad Hosein Sabzalian & Khalid A. Alattas & Fayez F. M. El-Sousy & Ardashir Mohammadzadeh & Saleh Mobayen & Mai The Vu & Mauricio Aredes, 2022. "A Neural Controller for Induction Motors: Fractional-Order Stability Analysis and Online Learning Algorithm," Mathematics, MDPI, vol. 10(6), pages 1-17, March.
    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. Xinsong Yang & Ruofeng Rao, 2023. "Well-Posedness, Dynamics, and Control of Nonlinear Differential System with Initial-Boundary Value," Mathematics, MDPI, vol. 11(10), pages 1-4, May.

    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. Lin Cao & Rongwei Guo, 2022. "Partial Anti-Synchronization Problem of the 4D Financial Hyper-Chaotic System with Periodically External Disturbance," Mathematics, MDPI, vol. 10(18), pages 1-14, September.
    2. Chang, Shuang & Wang, Yantao & Zhang, Xian & Wang, Xin, 2023. "A new method to study global exponential stability of inertial neural networks with multiple time-varying transmission delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 329-340.
    3. Xin Guo & Hejun Yao & Fangzheng Gao, 2022. "Global Prescribed-Time Stabilization of High-Order Nonlinear Systems with Asymmetric Actuator Dead-Zone," Mathematics, MDPI, vol. 10(12), pages 1-15, June.
    4. Wenjun Dong & Yujiao Huang & Tingan Chen & Xinggang Fan & Haixia Long, 2022. "Local Lagrange Exponential Stability Analysis of Quaternion-Valued Neural Networks with Time Delays," Mathematics, MDPI, vol. 10(13), pages 1-21, June.
    5. Ganesan, Bhuvaneshwari & Annamalai, Manivannan, 2023. "Anti-synchronization analysis of chaotic neural networks using delay product type looped-Lyapunov functional," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    6. Abdurahman, Abdujelil & Abudusaimaiti, Mairemunisa & Jiang, Haijun, 2023. "Fixed/predefined-time lag synchronization of complex-valued BAM neural networks with stochastic perturbations," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    7. Kumar, Ankit & Das, Subir & Singh, Sunny & Rajeev,, 2023. "Quasi-projective synchronization of inertial complex-valued recurrent neural networks with mixed time-varying delay and mismatched parameters," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    8. Deng, Jie & Li, Hong-Li & Cao, Jinde & Hu, Cheng & Jiang, Haijun, 2023. "State estimation for discrete-time fractional-order neural networks with time-varying delays and uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    9. Yaning Yu & Ziye Zhang, 2022. "State Estimation for Complex-Valued Inertial Neural Networks with Multiple Time Delays," Mathematics, MDPI, vol. 10(10), pages 1-14, May.
    10. Zheng, Yi & Wu, Xiaoqun & Fan, Ziye & Wang, Wei, 2022. "Identifying topology and system parameters of fractional-order complex dynamical networks," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    11. Guo, Runan & Xu, Shengyuan, 2023. "Observer-based sliding mode synchronization control of complex-valued neural networks with inertial term and mixed time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    12. Zhang, Hai & Cheng, Yuhong & Zhang, Weiwei & Zhang, Hongmei, 2023. "Time-dependent and Caputo derivative order-dependent quasi-uniform synchronization on fuzzy neural networks with proportional and distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 846-857.
    13. Pishro, Aboozar & Shahrokhi, Mohammad & Sadeghi, Hamed, 2022. "Fault-tolerant adaptive fractional controller design for incommensurate fractional-order nonlinear dynamic systems subject to input and output restrictions," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    14. Juan Yu & Kailong Xiong & Cheng Hu, 2024. "Synchronization Analysis for Quaternion-Valued Delayed Neural Networks with Impulse and Inertia via a Direct Technique," Mathematics, MDPI, vol. 12(7), pages 1-22, March.
    15. Ben Makhlouf, Abdellatif & Benjemaa, Mondher & Boucenna, Djalal & Hammami, Mohamed Ali, 2023. "Darboux problem for proportional partial fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    16. Rathinasamy, Anandaraman & Mayavel, Pichamuthu, 2023. "The balanced split step theta approximations of stochastic neutral Hopfield neural networks with time delay and Poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 455(C).
    17. Cheng Peng & Jiaxin Ma & Qiankun Li & Shang Gao, 2022. "Noise-to-State Stability in Probability for Random Complex Dynamical Systems on Networks," Mathematics, MDPI, vol. 10(12), pages 1-11, June.
    18. Priyanka, K. Sri Raja & Soundararajan, G. & Kashkynbayev, Ardak & Nagamani, G., 2023. "Exponential H∞ synchronization and anti-synchronization of delayed discrete-time complex-valued neural networks with uncertainties," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 301-321.
    19. Fahimeh Shiravani & Patxi Alkorta & Jose Antonio Cortajarena & Oscar Barambones, 2022. "An Integral Sliding Mode Stator Current Control for Industrial Induction Motor," Mathematics, MDPI, vol. 10(15), pages 1-20, August.
    20. Chengqiang Wang & Xiangqing Zhao & Can Wang & Zhiwei Lv, 2023. "Synchronization of Takagi–Sugeno Fuzzy Time-Delayed Stochastic Bidirectional Associative Memory Neural Networks Driven by Brownian Motion in Pre-Assigned Settling Time," Mathematics, MDPI, vol. 11(17), pages 1-32, August.

    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:gam:jmathe:v:10:y:2022:i:24:p:4823-:d:1007796. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.