A nonlinear version of the distributed Halanay inequality and its application

Nasser eddine Tatar, Rathinasamy Sakthivel*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this paper, first we prove a nonlinear version of Halanay inequality with distributed delay. Then, we use it to establish a local exponential stability result for a problem appearing in neural networks theory under the name Hopfield neural network system. This is done for activation functions violating the usual standard condition of Lipschitz continuity. One of the activation functions may be non-Lipschitz continuous. Finally, an example is provided to illustrate the developed theory.

Original languageEnglish
Pages (from-to)2190-2203
Number of pages14
JournalMathematical Methods in the Applied Sciences
Issue number4
StatePublished - 15 Mar 2022

Bibliographical note

Publisher Copyright:
© 2021 John Wiley & Sons, Ltd.


  • Hopfield neural network
  • Non-Lipschitz continuous activation functions
  • exponential stabilization
  • nonlinear Halanay inequality

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering


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