Coexistence and local μ-stability of multiple equilibrium points for memristive neural networks with nonmonotonic piecewise linear activation functions and unbounded time-varying delays. (December 2016)

• Record Type: Journal Article
• Authors: Nie, Xiaobing; Zheng, Wei Xing; Cao, Jinde
• Is Part Of: Neural networks. Volume 84(2016)
• Page Start: 172
• Page End: 180
• Publication Date: 2016-12
• Subjects: Memristive neural networks -- Multistability -- μ-stability -- Nonmonotonic piecewise linear activation functions -- Unbounded time delays; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; Neural networks (Neurobiology) -- Periodicals; Nervous System -- Periodicals; Ordinateurs neuronaux -- Périodiques; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux neuronaux (Neurobiologie) -- Périodiques; Neural computers; Neural networks (Computer science); Neural networks (Neurobiology); Periodicals; 006.32
• DOI: 10.1016/j.neunet.2016.08.006
• Languages: English
• ISSNs: 0893-6080

Abstract

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 5 n equilibrium points located in ℜ n, and 3 n of 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.