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An Analysis of Stability of a Class of Neutral‐Type Neural Networks with Discrete Time Delays

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  • Zeynep Orman
  • Sabri Arik

Abstract

The problem of existence, uniqueness, and global asymptotic stability is considered for the class of neutral‐type neural network model with discrete time delays. By employing a suitable Lyapunov functional and using the homeomorphism mapping theorem, we derive some new delay‐independent sufficient conditions for the existence, uniqueness, and global asymptotic stability of the equilibrium point for this class of neutral‐type systems. The obtained conditions basically establish some norm and matrix inequalities involving the network parameters of the neural system. The main advantage of the proposed results is that they can be expressed in terms of network parameters only. Some comparative examples are also given to compare our results with the previous corresponding results and demonstrate the effectiveness of the results presented.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:143585
    DOI: 10.1155/2013/143585
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    References listed on IDEAS

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    1. Tetie Pan & Bao Shi & Jian Yuan, 2012. "Global Stability of Almost Periodic Solution of a Class of Neutral-Type BAM Neural Networks," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-18, December.
    2. Guoquan Liu & Shumin Zhou & He Huang, 2012. "New LMI‐Based Conditions on Neural Networks of Neutral Type with Discrete Interval Delays and General Activation Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Ya Zhang & Bo Song & Ju H. Park & Zheng-Guang Wu, 2012. "Global Synchronization of Neutral‐Type Stochastic Delayed Complex Networks," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Ya Zhang & Bo Song & Ju H. Park & Zheng-Guang Wu, 2012. "Global Synchronization of Neutral-Type Stochastic Delayed Complex Networks," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-19, December.
    5. Tetie Pan & Bao Shi & Jian Yuan, 2012. "Global Stability of Almost Periodic Solution of a Class of Neutral‐Type BAM Neural Networks," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    6. Guoquan Liu & Shumin Zhou & He Huang, 2012. "New LMI-Based Conditions on Neural Networks of Neutral Type with Discrete Interval Delays and General Activation Functions," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, November.
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    Cited by:

    1. 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).
    2. 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).
    3. 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).
    4. 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).

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