IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i11p1055-d283429.html
   My bibliography  Save this article

Existence, Uniqueness and Exponential Stability of Periodic Solution for Discrete-Time Delayed BAM Neural Networks Based on Coincidence Degree Theory and Graph Theoretic Method

Author

Listed:
  • Manickam Iswarya

    (Department of Mathematics, Alagappa University, Karaikudi 630 004, India)

  • Ramachandran Raja

    (Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi 630 004, India)

  • Grienggrai Rajchakit

    (Department of Mathematics, Maejo University, Chiangmai 50290, Thailand)

  • Jinde Cao

    (School of Mathematics, Southeast University, Nanjing 211189, China)

  • Jehad Alzabut

    (Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia)

  • Chuangxia Huang

    (Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Department of Applied Mathematics, Changsha University of Science and Technology, Changsha 410114, China)

Abstract

In this work, a general class of discrete time bidirectional associative memory (BAM) neural networks (NNs) is investigated. In this model, discrete and continuously distributed time delays are taken into account. By utilizing this novel method, which incorporates the approach of Kirchhoff’s matrix tree theorem in graph theory, Continuation theorem in coincidence degree theory and Lyapunov function, we derive a few sufficient conditions to ensure the existence, uniqueness and exponential stability of the periodic solution of the considered model. At the end of this work, we give a numerical simulation that shows the effectiveness of this work.

Suggested Citation

  • Manickam Iswarya & Ramachandran Raja & Grienggrai Rajchakit & Jinde Cao & Jehad Alzabut & Chuangxia Huang, 2019. "Existence, Uniqueness and Exponential Stability of Periodic Solution for Discrete-Time Delayed BAM Neural Networks Based on Coincidence Degree Theory and Graph Theoretic Method," Mathematics, MDPI, vol. 7(11), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1055-:d:283429
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/11/1055/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/11/1055/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yuan Huang & Xiaochun Chen & Huiming Zhu & Chuangxia Huang & Zhongchu Tian, 2019. "The Heterogeneous Effects of FDI and Foreign Trade on CO 2 Emissions: Evidence from China," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-14, January.
    2. Chuangxia Huang & Jie Cao & Fenghua Wen & Xiaoguang Yang, 2016. "Stability Analysis of SIR Model with Distributed Delay on Complex Networks," PLOS ONE, Public Library of Science, vol. 11(8), pages 1-22, August.
    3. Chao Yang & Lihong Huang & Fangmin Li, 2018. "Exponential Synchronization Control of Discontinuous Nonautonomous Networks and Autonomous Coupled Networks," Complexity, Hindawi, vol. 2018, pages 1-10, October.
    4. Maharajan, C. & Raja, R. & Cao, Jinde & Rajchakit, G. & Tu, Zhengwen & Alsaedi, Ahmed, 2018. "LMI-based results on exponential stability of BAM-type neural networks with leakage and both time-varying delays: A non-fragile state estimation approach," Applied Mathematics and Computation, Elsevier, vol. 326(C), pages 33-55.
    5. Zhang, Xinhong & Li, Wenxue & Wang, Ke, 2015. "The existence and global exponential stability of periodic solution for a neutral coupled system on networks with delays," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 208-217.
    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. 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.
    2. Chen, Dazhao & Zhang, Zhengqiu, 2022. "Finite-time synchronization for delayed BAM neural networks by the approach of the same structural functions," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Tranthi, Janejira & Botmart, Thongchai & Weera, Wajaree & La-inchua, Teerapong & Pinjai, Sirada, 2022. "New results on robust exponential stability of Takagi–Sugeno fuzzy for neutral differential systems with mixed time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 714-738.

    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. Yang, Xin & Wen, Shigang & Zhao, Xian & Huang, Chuangxia, 2020. "Systemic importance of financial institutions: A complex network perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. Xin Yang & Shigang Wen & Zhifeng Liu & Cai Li & Chuangxia Huang, 2019. "Dynamic Properties of Foreign Exchange Complex Network," Mathematics, MDPI, vol. 7(9), pages 1-19, September.
    3. 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.
    4. Xu, Changjin & Liao, Maoxin & Li, Peiluan & Yuan, Shuai, 2021. "Impact of leakage delay on bifurcation in fractional-order complex-valued neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Hayat Khan & Liu Weili & Itbar Khan, 2022. "Environmental innovation, trade openness and quality institutions: an integrated investigation about environmental sustainability," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 24(3), pages 3832-3862, March.
    6. 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).
    7. Mohd Shahidan Shaari & Muhamad Huzaifah Asbullah & Noorazeela Zainol Abidin & Zulkefly Abdul Karim & Benjamin Nangle, 2023. "Determinants of Foreign Direct Investment in ASEAN+3 Countries: The Role of Environmental Degradation," IJERPH, MDPI, vol. 20(3), pages 1-14, January.
    8. 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.
    9. Devesh Singh & Sunil Kumar Dhiman, 2023. "The linkage between carbon emissions, foreign direct investment, economic growth, and gross value added," Journal of Environmental Studies and Sciences, Springer;Association of Environmental Studies and Sciences, vol. 13(1), pages 156-176, March.
    10. Duan, Wenyong & Li, Yan & Sun, Yi & Chen, Jian & Yang, Xiaodong, 2020. "Enhanced master–slave synchronization criteria for chaotic Lur’e systems based on time-delayed feedback control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 276-294.
    11. Jihong Xiao & Xuehong Zhu & Chuangxia Huang & Xiaoguang Yang & Fenghua Wen & Meirui Zhong, 2019. "A New Approach for Stock Price Analysis and Prediction Based on SSA and SVM," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 287-310, January.
    12. Balasundaram, K. & Raja, R. & Pratap, A. & Chandrasekaran, S., 2019. "Impulsive effects on competitive neural networks with mixed delays: Existence and exponential stability analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 290-302.
    13. Oliveira, José J., 2022. "Global stability criteria for nonlinear differential systems with infinite delay and applications to BAM neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    14. Zhang, Shuai & Yang, Yongqing & Sui, Xin & Xu, Xianyu, 2019. "Finite-time synchronization of memristive neural networks with parameter uncertainties via aperiodically intermittent adjustment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    15. Fredrick Oteng Agyeman & Ma Zhiqiang & Mingxing Li & Agyemang Kwasi Sampene & Malcom Frimpong Dapaah & Emmanuel Adu Gyamfi Kedjanyi & Paul Buabeng & Yiyao Li & Saifullah Hakro & Mohammad Heydari, 2022. "Probing the Effect of Governance of Tourism Development, Economic Growth, and Foreign Direct Investment on Carbon Dioxide Emissions in Africa: The African Experience," Energies, MDPI, vol. 15(13), pages 1-24, June.
    16. Irfan, Muhammad & Rehman, Mubeen Abdur & Razzaq, Asif & Hao, Yu, 2023. "What derives renewable energy transition in G-7 and E-7 countries? The role of financial development and mineral markets," Energy Economics, Elsevier, vol. 121(C).
    17. Wang, Chao & Huang, Xia & Hu, Xiaoqian & Zhao, Longfeng & Liu, Chao & Ghadimi, Pezhman, 2021. "Trade characteristics, competition patterns and COVID-19 related shock propagation in the global solar photovoltaic cell trade," Applied Energy, Elsevier, vol. 290(C).
    18. Miaadi, Foued & Li, Xiaodi, 2021. "Impulse-dependent settling-time for finite time stabilization of uncertain impulsive static neural networks with leakage delay and distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 259-276.
    19. Liu, Qiming & Li, Hua, 2019. "Global dynamics analysis of an SEIR epidemic model with discrete delay on complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 289-296.
    20. Zhujia Yin & Yantuan Yu & Jianhuan Huang, 2018. "Evaluation and evolution of bank efficiency considering heterogeneity technology: An empirical study from China," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-19, October.

    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:7:y:2019:i:11:p:1055-:d:283429. 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.