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Almost Periodic Solutions for Neutral‐Type BAM Neural Networks with Delays on Time Scales

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  • Yongkun Li
  • Li Yang

Abstract

Using the existence of the exponential dichotomy of linear dynamic equations on time scales, a fixed point theorem and the theory of calculus on time scales, we obtain some sufficient conditions for the existence and exponential stability of almost periodic solutions for a class of neutral‐type BAM neural networks with delays on time scales. Finally, a numerical example illustrates the feasibility of our results and also shows that the continuous‐time neural network and its discrete‐time analogue have the same dynamical behaviors. The results of this paper are completely new even if the time scale 𝕋 = ℝ or ℤ and complementary to the previously known results.

Suggested Citation

  • Yongkun Li & Li Yang, 2013. "Almost Periodic Solutions for Neutral‐Type BAM Neural Networks with Delays on Time Scales," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:942309
    DOI: 10.1155/2013/942309
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    References listed on IDEAS

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    1. Zheng, Baodong & Zhang, Yazhuo & Zhang, Chunrui, 2008. "Global existence of periodic solutions on a simplified BAM neural network model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1397-1408.
    2. Yongkun Li & Chao Wang, 2011. "Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    3. Xia, Yonghui & Cao, Jinde & Lin, Muren, 2007. "New results on the existence and uniqueness of almost periodic solution for BAM neural networks with continuously distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 928-936.
    4. Li, Yongkun, 2005. "Global exponential stability of BAM neural networks with delays and impulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 279-285.
    5. Yongkun Li & Chao Wang, 2011. "Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-22, October.
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    Cited by:

    1. Lili Zhao & Yongkun Li, 2014. "Global Exponential Stability of Weighted Pseudo‐Almost Periodic Solutions of Neutral Type High‐Order Hopfield Neural Networks with Distributed Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Li Yang & Yongkun Li & Wanqin Wu, 2014. "Cn‐Almost Periodic Functions and an Application to a Lasota‐Wazewska Model on Time Scales," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

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