IDEAS home Printed from https://ideas.repec.org/a/hin/complx/6292597.html
   My bibliography  Save this article

Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory

Author

Listed:
  • Ruofeng Rao
  • Shouming Zhong

Abstract

This paper investigates the stochastically exponential stability of reaction-diffusion impulsive stochastic cellular neural networks (CNN). The reaction-diffusion pulse stochastic system model characterizes the complexity of practical engineering and brings about mathematical difficulties, too. However, the difficulties have been overcome by constructing a new contraction mapping and an appropriate distance on a product space which is guaranteed to be a complete space. This is the first time to employ the fixed point theorem to derive the stability criterion of reaction-diffusion impulsive stochastic CNN with distributed time delays. Finally, an example is provided to illustrate the effectiveness of the proposed methods.

Suggested Citation

  • Ruofeng Rao & Shouming Zhong, 2017. "Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory," Complexity, Hindawi, vol. 2017, pages 1-9, September.
    • Handle: RePEc:hin:complx:6292597
    DOI: 10.1155/2017/6292597
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2017/6292597.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2017/6292597.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2017/6292597?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
    ---><---

    References listed on IDEAS

    as
    1. Ruofeng Rao & Zhilin Pu, 2013. "LMI-Based Stability Criterion of Impulsive T-S Fuzzy Dynamic Equations via Fixed Point Theory," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, September.
    2. Kwiecinska, Anna A., 1999. "Stabilization of partial differential equations by noise," Stochastic Processes and their Applications, Elsevier, vol. 79(2), pages 179-184, February.
    3. Li, Xiaodi & Deng, Feiqi, 2017. "Razumikhin method for impulsive functional differential equations of neutral type," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 41-49.
    Full references (including those not matched with items on IDEAS)

    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 Sun & Gui-Lai Zhang & Zhi-Wei Wang & Tao Liu, 2023. "Convergence of the Euler Method for Impulsive Neutral Delay Differential Equations," Mathematics, MDPI, vol. 11(22), pages 1-14, November.
    2. Wang, Pengfei & Zou, Wenqing & Su, Huan, 2019. "Stability of complex-valued impulsive stochastic functional differential equations on networks with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 338-354.
    3. Gui-Lai Zhang & Yang Sun & Ya-Xin Zhang & Chao Liu, 2024. "Euler Method for a Class of Linear Impulsive Neutral Differential Equations," Mathematics, MDPI, vol. 12(18), pages 1-19, September.
    4. Yunfeng Li & Pei Cheng & Zheng Wu, 2022. "Exponential Stability of Impulsive Neutral Stochastic Functional Differential Equations," Mathematics, MDPI, vol. 10(21), pages 1-17, November.
    5. Qian, Wei-Liang & F. Siqueira, Adriano & F. Machado, Romuel & Lin, Kai & Grant, Ted W., 2017. "Dynamical capacity drop in a nonlinear stochastic traffic model," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 328-339.
    6. Siqueira, Adriano F. & Peixoto, Carlos J.T. & Wu, Chen & Qian, Wei-Liang, 2016. "Effect of stochastic transition in the fundamental diagram of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 87(C), pages 1-13.
    7. Rößler, Andreas & Seaïd, Mohammed & Zahri, Mostafa, 2009. "Numerical simulation of stochastic replicator models in catalyzed RNA-like polymers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(12), pages 3577-3586.

    More about this item

    Statistics

    Access and download statistics

    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:hin:complx:6292597. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.