Multistability of neural networks with discontinuous non-monotonic piecewise linear activation functions and time-varying delays

Xiaobing Nie, Wei Xing Zheng

    Research output: Contribution to journalArticlepeer-review

    63 Citations (Scopus)

    Abstract

    This paper is concerned with the problem of coexistence and dynamical behaviors of multiple equilibrium points for neural networks with discontinuous non-monotonic piecewise linear activation functions and time-varying delays. The fixed point theorem and other analytical tools are used to develop certain sufficient conditions that ensure that the n-dimensional discontinuous neural networks with time-varying delays can have at least 5n equilibrium points, 3n of which are locally stable and the others are unstable. The importance of the derived results is that it reveals that the discontinuous neural networks can have greater storage capacity than the continuous ones. Moreover, different from the existing results on multistability of neural networks with discontinuous activation functions, the 3n locally stable equilibrium points obtained in this paper are located in not only saturated regions, but also unsaturated regions, due to the non-monotonic structure of discontinuous activation functions. A numerical simulation study is conducted to illustrate and support the derived theoretical results.
    Original languageEnglish
    Pages (from-to)65-79
    Number of pages15
    JournalNeural Networks
    Volume65
    DOIs
    Publication statusPublished - 2015

    Keywords

    • multistability
    • neural networks (computer science)
    • piecewise linear topology
    • time delay systems

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