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Global exponential stability of high-order Hopfield neural networks with state-dependent impulses

Author

Listed:
  • He, Zhilong
  • Li, Chuandong
  • Li, Hongfei
  • Zhang, Qiangqiang

Abstract

In this paper, we discuss the stability of high-order Hopfield neural networks with state-dependent impulses. Under some necessary assumptions, that every solution of the considered system intersects each impulsive surface exactly once is proved. Meanwhile, by using B-equivalence method, the considered system can be simplified to a system with fixed-time impulses. Moreover, some sufficient criteria are derived to ensure the stability between high-order Hopfield neural networks with state-dependent impulses and the corresponding system with fixed-time impulses. The main results show that the stability of high-order Hopfield neural networks with state-dependent impulses maintains no matter the stable continuous subsystems with unstabilizing impulses or the unstable continuous subsystems with stabilizing impulses. Finally, some numerical examples are given to illustrate the effectiveness of our results.

Suggested Citation

  • He, Zhilong & Li, Chuandong & Li, Hongfei & Zhang, Qiangqiang, 2020. "Global exponential stability of high-order Hopfield neural networks with state-dependent impulses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
  • Handle: RePEc:eee:phsmap:v:542:y:2020:i:c:s037843711931917x
    DOI: 10.1016/j.physa.2019.123434
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    References listed on IDEAS

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    3. Nie, Linfei & Teng, Zhidong & Hu, Lin & Peng, Jigen, 2009. "Existence and stability of periodic solution of a predator–prey model with state-dependent impulsive effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2122-2134.
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