Multiple Mittag-Leffler Stability of Fractional-Order Recurrent Neural Networks

Peng Liu, Zhigang Zeng, Jun Wang

Research output: Contribution to journalArticlepeer-review

127 Citations (Scopus)


In this paper, coexistence and stability of multiple equilibrium points of fractional-order recurrent neural networks are addressed. Several sufficient conditions are derived for ascertaining the existence of ∏i=1n(2Ki+1) equilibrium points (Ki≥0) and the local Mittag-Leffler stability of ∏i=1n(Ki+1) equilibrium points of them by using the geometrical properties of activation functions and algebraic properties of nonsingular M-matrix. In contrast with many existing results, the derived results cover both mono-stability and multistability, and the activation functions herein could be nonmonotonic and nonlinear in any open interval. In addition, three numerical examples are elaborated to substantiate the efficacy and characteristics of the theoretical results.

Original languageEnglish
Article number7831495
Pages (from-to)2279-2288
Number of pages10
JournalIEEE Transactions on Systems, Man, and Cybernetics: Systems
Issue number8
Publication statusPublished - Aug 2017
Externally publishedYes


  • Fractional-order recurrent neural networks
  • Mittag-Leffler stability
  • multistability


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