Multistability of Recurrent Neural Networks with Nonmonotonic Activation Functions and Mixed Time Delays

Peng Liu, Zhigang Zeng, Jun Wang

Research output: Contribution to journalArticlepeer-review

88 Citations (Scopus)


This paper presents new theoretical results on the multistability analysis of a class of recurrent neural networks with nonmonotonic activation functions and mixed time delays. Several sufficient conditions are derived for ascertaining the existence of 3n equilibrium points and the exponential stability of 2n equilibrium points via state space partition by using the geometrical properties of activation functions and algebraic properties of nonsingular M-matrix. Compared with existing results, the conditions herein are much more computable with one order less linear matrix inequalities. Furthermore, the attraction basins of these exponentially stable equilibrium points are estimated. It is revealed that the attraction basins of the 2n equilibrium points can be larger than their originally partitioned subspaces. Three numerical examples are elaborated with typical nonmonotonic activation functions to substantiate the efficacy and characteristics of the theoretical results.

Original languageEnglish
Article number7185449
Pages (from-to)512-523
Number of pages12
JournalIEEE Transactions on Systems, Man, and Cybernetics: Systems
Issue number4
Publication statusPublished - Apr 2016
Externally publishedYes


  • Mixed time delays
  • multistability
  • nonmonotonic activation functions
  • recurrent neural networks


Dive into the research topics of 'Multistability of Recurrent Neural Networks with Nonmonotonic Activation Functions and Mixed Time Delays'. Together they form a unique fingerprint.

Cite this