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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
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    References listed on IDEAS

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    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. 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.
    4. 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.
    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.
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    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.

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