title: Multistability of neural networks with discontinuous non-monotonic piecewise linear activation functions and time-varying delays.
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 5(n) equilibrium points, 3(n) 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 3(n) 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.
authors.affiliation: Department of Mathematics, Southeast University, Nanjing 210096, China; School of Computing, Engineering and Mathematics, University of Western Sydney, Sydney NSW 2751, Australia. Electronic address: xbnie@seu.edu.cn.
authors.forename: Xiaobing
authors.initials: X
authors.lastname: Nie
authors.affiliation: School of Computing, Engineering and Mathematics, University of Western Sydney, Sydney NSW 2751, Australia. Electronic address: w.zheng@uws.edu.au.
authors.forename: Wei Xing
authors.initials: WX
authors.lastname: Zheng
mesh_terms: D000465:Algorithms; D016571:Neural Networks, Computer; D013997:Time Factors
keywords: Discontinuous non-monotonic piecewise linear activation functions; Instability; Multistability; Neural networks; Time-varying delays