Some sufficient conditions for global exponential stability of delayed Hopfield neural networks

Hongtao Lu, Fu Lai Korris Chung, Zhenya He

Research output: Journal article publicationJournal articleAcademic researchpeer-review

41 Citations (Scopus)

Abstract

In this paper, we have derived some sufficient conditions for existence and uniqueness of equilibrium and global exponential stability in delayed Hopfield neural networks by using a different approach from the usually used one where the existence, uniqueness of equilibrium and stability are proved in two separate steps, rather we first prove global exponential convergence to 0 of the difference between any two solutions of the original neural networks, the existence and uniqueness of equilibrium is the direct results of this procedure. We obtain the conditions by suitable construction of Lyapunov functionals and estimation of derivates of the Lyapunov functionals by the well-known Young's inequality and Holder's inequality. The proposed conditions are related to p-norms of vector or matrix, p∈[1,∞], and thus unify and generalize some results in the literature.
Original languageEnglish
Pages (from-to)537-544
Number of pages8
JournalNeural Networks
Volume17
Issue number4
DOIs
Publication statusPublished - 1 May 2004

Keywords

  • Delayed Hopfield neural networks
  • Global exponential stability
  • p -Norms

ASJC Scopus subject areas

  • Cognitive Neuroscience
  • Artificial Intelligence

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