IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2014y2014i1n145061.html

Existence and Exponential Stability of Solutions for Stochastic Cellular Neural Networks with Piecewise Constant Argument

Author

Listed:
  • Xiaoai Li

Abstract

By using the concept of differential equations with piecewise constant argument of generalized type, a model of stochastic cellular neural networks with piecewise constant argument is developed. Sufficient conditions are obtained for the existence and uniqueness of the equilibrium point for the addressed neural networks. pth moment exponential stability is investigated by means of Lyapunov functional, stochastic analysis, and inequality technique. The results in this paper improve and generalize some of the previous ones. An example with numerical simulations is given to illustrate our results.

Suggested Citation

  • Xiaoai Li, 2014. "Existence and Exponential Stability of Solutions for Stochastic Cellular Neural Networks with Piecewise Constant Argument," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:145061
    DOI: 10.1155/2014/145061
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/145061
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/145061?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. S. M. Shah & Joseph Wiener, 1983. "Advanced differential equations with piecewise constant argument deviations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 6, pages 1-33, January.
    2. Xiao Liang & Linshan Wang, 2012. "Exponential Stability for a Class of Stochastic Reaction-Diffusion Hopfield Neural Networks with Delays," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-12, March.
    3. Sabri Arik & Juhyun Park & Tingwen Huang & José J. Oliveira, 2013. "Analysis of Nonlinear Dynamics of Neural Networks," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Zeynep Orman & Sabri Arik, 2013. "An Analysis of Stability of a Class of Neutral‐Type Neural Networks with Discrete Time Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Zeynep Orman & Sabri Arik, 2013. "An Analysis of Stability of a Class of Neutral-Type Neural Networks with Discrete Time Delays," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, June.
    6. Sabri Arik & Juhyun Park & Tingwen Huang & José J. Oliveira, 2013. "Analysis of Nonlinear Dynamics of Neural Networks," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-1, March.
    7. Guowei Yang & Yonggui Kao & Changhong Wang, 2013. "Exponential Stability and Periodicity of Fuzzy Delayed Reaction-Diffusion Cellular Neural Networks with Impulsive Effect," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, March.
    8. Guowei Yang & Yonggui Kao & Changhong Wang, 2013. "Exponential Stability and Periodicity of Fuzzy Delayed Reaction‐Diffusion Cellular Neural Networks with Impulsive Effect," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    9. Xiao Liang & Linshan Wang, 2012. "Exponential Stability for a Class of Stochastic Reaction‐Diffusion Hopfield Neural Networks with Delays," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    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. Marat Akhmet & Zakhira Nugayeva & Roza Seilova, 2025. "Alpha Unpredictable Cohen–Grossberg Neural Networks with Poisson Stable Piecewise Constant Arguments," Mathematics, MDPI, vol. 13(7), pages 1-27, March.

    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. Yonggui Kao & Hamid Reza Karimi, 2014. "Stability in Mean of Partial Variables for Coupled Stochastic Reaction‐Diffusion Systems on Networks: A Graph Approach," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Jianmin Duan & Manfeng Hu & Yongqing Yang & Liuxiao Guo, 2013. "Stability Analysis of Stochastic Markovian Jump Neural Networks with Different Time Scales and Randomly Occurred Nonlinearities Based on Delay‐Partitioning Projection Approach," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Hai Zhang & Daiyong Wu & Jinde Cao, 2014. "Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Ruofeng Rao & Zhilin Pu & Shouming Zhong & Jialin Huang, 2013. "On the Role of Diffusion Behaviors in Stability Criterion for p‐Laplace Dynamical Equations with Infinite Delay and Partial Fuzzy Parameters under Dirichlet Boundary Value," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    5. Xueying Shao & Qing Lu & Hamid Reza Karimi & Jin Zhu, 2014. "New Results on Passivity Analysis for Uncertain Neural Networks with Time‐Varying Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    6. Ruofeng Rao & Xiongrui Wang & Shouming Zhong & Zhilin Pu, 2013. "LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian‐Jumping Cohen‐Grossberg Neural Networks with Nonlinear p‐Laplace Diffusion," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    7. Xiongrui Wang & Ruofeng Rao & Shouming Zhong, 2012. "LMI Approach to Stability Analysis of Cohen‐Grossberg Neural Networks with p‐Laplace Diffusion," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    8. Chunge Lu & Linshan Wang, 2014. "Robust Exponential Stability of Impulsive Stochastic Neural Networks with Leakage Time‐Varying Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    9. Han Yan & Shufang Ma & Yanbin Liu & Hongquan Sun, 2012. "Convergence and Stability in Collocation Methods of Equation u′(t) = au(t) + bu([t])," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    10. Qi Wang & Jiechang Wen & Shenshan Qiu, 2013. "Euler‐Maclaurin Method for Linear Differential Equations with Piecewise Constant Arguments with One Delay: Stability and Oscillations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    11. Minghui Song & M. Z. Liu, 2012. "Stability of Analytic and Numerical Solutions for Differential Equations with Piecewise Continuous Arguments," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    12. Zhijian Wei, 2011. "Periodicity in a Class of Systems of Delay Difference Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    13. Kuo-Shou Chiu, 2013. "Existence and Global Exponential Stability of Equilibrium for Impulsive Cellular Neural Network Models with Piecewise Alternately Advanced and Retarded Argument," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    14. James Guyker, 2015. "Periodic Solutions of Certain Differential Equations with Piecewise Constant Argument," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-17, July.
    15. Changjin Xu, 2012. "Neimark‐Sacker Bifurcation Analysis for a Discrete‐Time System of Two Neurons," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    16. Phu, Nguyen Dinh & Phut, Lai Van & Van Hoa, Ngo, 2026. "Solving fuzzy non-homogeneous linear differential systems with piecewise constant arguments involving the short-memory variable-order Caputo fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 510(C).
    17. Assanova, Anar T. & Uteshova, Roza, 2022. "Solution of a nonlocal problem for hyperbolic equations with piecewise constant argument of generalized type," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    18. Hartung, Ferenc, 2022. "On numerical approximation of a delay differential equation with impulsive self-support condition," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    19. Haihua Liang & Gen-qiang Wang, 2012. "Oscillation Criteria of Certain Third‐Order Differential Equation with Piecewise Constant Argument," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).

    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:wly:jnljam:v:2014:y:2014:i:1:n:145061. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    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.