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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… (More)

In this paper, second-order interactions are introduced into competitive neural networks (NNs) and the multistability is discussed for second-order competitive NNs (SOCNNs) with nondecreasing saturated activation functions. Firstly, based on decomposition of state space, Cauchy convergence principle, and inequality technique, some sufficient conditions… (More)

Keywords: Delayed competitive neural networks Multistability Instability Piecewise linear activation functions a b s t r a c t In this paper, we investigate the exact existence and dynamical behaviors of multiple equilibrium points for delayed competitive neural networks (DCNNs) with a class of nondecreasing piecewise linear activation functions with… (More)

The problem of coexistence and dynamical behaviors of multiple equilibrium points is addressed for a class of memristive Cohen-Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays. By virtue of the fixed point theorem, nonsmooth analysis theory and other analytical tools, some sufficient conditions are… (More)

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… (More)

This paper addresses the problem of coexistence and dynamical behaviors of multiple equilibria for competitive neural networks. First, a general class of discontinuous nonmonotonic piecewise linear activation functions is introduced for competitive neural networks. Then based on the fixed point theorem and theory of strict diagonal dominance matrix, it is… (More)