Multistability for delayed neural networks via sequential contracting

Chang Yuan Cheng, Kuang Hui Lin, Chih-Wen Shih, Jui Pin Tseng

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


In this paper, we explore a variety of new multistability scenarios in the general delayed neural network system. Geometric structure embedded in equations is exploited and incorporated into the analysis to elucidate the underlying dynamics. Criteria derived from different geometric configurations lead to disparate numbers of equilibria. A new approach named sequential contracting is applied to conclude the global convergence to multiple equilibrium points of the system. The formulation accommodates both smooth sigmoidal and piecewiselinear activation functions. Several numerical examples illustrate the present analytic theory.

Original languageEnglish
Article number7053938
Pages (from-to)3109-3122
Number of pages14
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number12
StatePublished - 1 Dec 2015


  • Complete stability
  • Delay equations
  • Multistability
  • Neural network


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