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The Existence and Global Exponential Stability of Almost Periodic Solutions for Neutral-Type CNNs on Time Scales

Author

Listed:
  • Bing Li

    (School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, Yunnan, China)

  • Yongkun Li

    (Department of Mathematics, Yunnan University, Kunming 650091, Yunnan, China)

  • Xiaofang Meng

    (Department of Mathematics, Yunnan University, Kunming 650091, Yunnan, China)

Abstract

In this paper, neutral-type competitive neural networks with mixed time-varying delays and leakage delays on time scales are proposed. Based on the contraction fixed-point theorem, some sufficient conditions that are independent of the backwards graininess function of the time scale are obtained for the existence and global exponential stability of almost periodic solutions of neural networks under consideration. The results obtained are brand new, indicating that the continuous time and discrete-time conditions of the network share the same dynamic behavior. Finally, two examples are given to illustrate the validity of the results obtained.

Suggested Citation

  • Bing Li & Yongkun Li & Xiaofang Meng, 2019. "The Existence and Global Exponential Stability of Almost Periodic Solutions for Neutral-Type CNNs on Time Scales," Mathematics, MDPI, vol. 7(4), pages 1-25, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:321-:d:218269
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    References listed on IDEAS

    as
    1. Yongkun Li & Xiaofang Meng, 2017. "Existence and Global Exponential Stability of Pseudo Almost Periodic Solutions for Neutral Type Quaternion-Valued Neural Networks with Delays in the Leakage Term on Time Scales," Complexity, Hindawi, vol. 2017, pages 1-15, December.
    2. 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.
    3. Xu, Changjin & Li, Peiluan, 2017. "Global exponential convergence of neutral-type Hopfield neural networks with multi-proportional delays and leakage delays," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 139-144.
    4. Gisèle Mophou & Gaston Mandata N’Guérékata & Aril Milce, 2014. "Almost Automorphic Functions of Order and Applications to Dynamic Equations on Time Scales," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-13, December.
    Full references (including those not matched with items on IDEAS)

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