title: Coexistence and local μ-stability of multiple equilibrium points for memristive neural networks with nonmonotonic piecewise linear activation functions and unbounded time-varying delays.
abstract: In this paper, the coexistence and dynamical behaviors of multiple equilibrium points are discussed for a class of memristive neural networks (MNNs) with unbounded time-varying delays and nonmonotonic piecewise linear activation functions. By means of the fixed point theorem, nonsmooth analysis theory and rigorous mathematical analysis, it is proven that under some conditions, such n-neuron MNNs can have 5nequilibrium points located in ℜn, and 3nof them are locally μ-stable. As a direct application, some criteria are also obtained on the multiple exponential stability, multiple power stability, multiple log-stability and multiple log-log-stability. All these results reveal that the addressed neural networks with activation functions introduced in this paper can generate greater storage capacity than the ones with Mexican-hat-type activation function. Numerical simulations are presented to substantiate the theoretical results.
authors: Department of Mathematics, Southeast University, Nanjing 210096, China; School of Computing, Engineering and Mathematics, Western Sydney University, Sydney, NSW 2751, Australia. Electronic address: xbnie@seu.edu.cn.
authors: Xiaobing
authors: X
authors: Nie
authors: School of Computing, Engineering and Mathematics, Western Sydney University, Sydney, NSW 2751, Australia. Electronic address: w.zheng@westernsydney.edu.au.
authors: Wei Xing
authors: WX
authors: Zheng
authors: Department of Mathematics, Southeast University, Nanjing 210096, China. Electronic address: jdcao@seu.edu.cn.
authors: Jinde
authors: J
authors: Cao
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D016014:Linear Models; D016571:Neural Networks, Computer; D009474:Neurons; D013997:Time Factors
keywords: -stability; Memristive neural networks; Multistability; Nonmonotonic piecewise linear activation functions; Unbounded time delays