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Periodic Solutions for Shunting Inhibitory Cellular Neural Networks of Neutral Type with Time‐Varying Delays in the Leakage Term on Time Scales

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  • Yongkun Li
  • Lei Wang
  • Yu Fei

Abstract

A class of shunting inhibitory cellular neural networks of neutral type with time‐varying delays in the leakage term on time scales is proposed. Based on the exponential dichotomy of linear dynamic equations on time scales, fixed point theorems, and calculus on time scales we obtain some sufficient conditions for the existence and global exponential stability of periodic solutions for that class of neural networks. The results of this paper are completely new and complementary to the previously known results even if the time scale 𝕋 = ℝ or ℤ. Moreover, we present illustrative numerical examples to show the feasibility of our results.

Suggested Citation

  • Yongkun Li & Lei Wang & Yu Fei, 2014. "Periodic Solutions for Shunting Inhibitory Cellular Neural Networks of Neutral Type with Time‐Varying Delays in the Leakage Term on Time Scales," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:496396
    DOI: 10.1155/2014/496396
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    References listed on IDEAS

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    1. Park, Ju H., 2009. "Synchronization of cellular neural networks of neutral type via dynamic feedback controller," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1299-1304.
    2. Xia, Yonghui & Cao, Jinde & Huang, Zhenkun, 2007. "Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1599-1607.
    3. Park, Ju H. & Kwon, O.M., 2009. "Global stability for neural networks of neutral-type with interval time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1174-1181.
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