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Synchronization in Array of Coupled Neural Networks with Unbounded Distributed Delay and Limited Transmission Efficiency

Author

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  • Xinsong Yang
  • Mengzhe Zhou
  • Jinde Cao

Abstract

This paper investigates global synchronization in an array of coupled neural networks with time‐varying delays and unbounded distributed delays. In the coupled neural networks, limited transmission efficiency between coupled nodes, which makes the model more practical, is considered. Based on a novel integral inequality and the Lyapunov functional method, sufficient synchronization criteria are derived. The derived synchronization criteria are formulated by linear matrix inequalities (LMIs) and can be easily verified by using Matlab LMI Toolbox. It is displayed that, when some of the transmission efficiencies are limited, the dynamics of the synchronized state are different from those of the isolated node. Furthermore, the transmission efficiency and inner coupling matrices between nodes play important roles in the final synchronized state. The derivative of the time‐varying delay can be any given value, and the time‐varying delay can be unbounded. The outer‐coupling matrices can be symmetric or asymmetric. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results.

Suggested Citation

  • Xinsong Yang & Mengzhe Zhou & Jinde Cao, 2013. "Synchronization in Array of Coupled Neural Networks with Unbounded Distributed Delay and Limited Transmission Efficiency," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:402031
    DOI: 10.1155/2013/402031
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    References listed on IDEAS

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    1. Xinsong Yang & Chuangxia Huang & Zhichun Yang, 2012. "Stochastic Synchronization of Reaction-Diffusion Neural Networks under General Impulsive Controller with Mixed Delays," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, December.
    2. Li, Tao & Fei, Shu-min & Zhang, Kan-jian, 2008. "Synchronization control of recurrent neural networks with distributed delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 982-996.
    3. Xinsong Yang & Chuangxia Huang & Zhichun Yang, 2012. "Stochastic Synchronization of Reaction‐Diffusion Neural Networks under General Impulsive Controller with Mixed Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Yu, Wenwu & Cao, Jinde, 2007. "Synchronization control of stochastic delayed neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 252-260.
    5. Ping Zhou & Rui Ding, 2012. "Modified Function Projective Synchronization between Different Dimension Fractional-Order Chaotic Systems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, September.
    6. Cao, Jinde & Wang, Zidong & Sun, Yonghui, 2007. "Synchronization in an array of linearly stochastically coupled networks with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 718-728.
    7. Ping Zhou & Rui Ding, 2012. "Modified Function Projective Synchronization between Different Dimension Fractional‐Order Chaotic Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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