Multiple almost periodic solutions in nonautonomous delayed neural networks
Neural Computation
Complete stability in multistable delayed neural networks
Neural Computation
Multistability and new attraction basins of almost-periodic solutions of delayed neural networks
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Multistability in networks with self-excitation and high-order synaptic connectivity
IEEE Transactions on Circuits and Systems Part I: Regular Papers
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Global exponential stability of competitive neural networks with different time scales
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Multiperiodicity of Discrete-Time Delayed Neural Networks Evoked by Periodic External Inputs
IEEE Transactions on Neural Networks
Global Exponential Stability of Multitime Scale Competitive Neural Networks With Nonsmooth Functions
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
On Attracting Basins of Multiple Equilibria of a Class of Cellular Neural Networks
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
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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 2r(r=1) corner points. It is shown that under some conditions, the N-neuron DCNNs can have and only have (2r+1)^N equilibrium points, (r+1)^N of which are locally exponentially stable, based on decomposition of state space, fixed point theorem and matrix theory. In addition, for the activation function with two corner points, the dynamical behaviors of all equilibrium points for 2-neuron delayed Hopfield neural networks(DHNNs) are completely analyzed, and a sufficient criterion derived for ensuring the networks have exactly nine equilibrium points, four of which are stable and others are unstable, by discussing the distribution of roots of the corresponding characteristic equation of the linearized delayed system. Finally, two examples with their simulations are presented to verify the theoretical analysis.