A comment on "On equilibria, stability, and instability of Hopfield neural networks"

Global Exponential Stability of Multitime Scale Competitive Neural Networks With Nonsmooth Functions

In this paper, we study the global exponential stability of a multitime scale competitive neural network model with nonsmooth functions, which models a literally inhibited neural network with unsupervised Hebbian learning. The network has two types of state variables, one corresponds to the fast neural activity and another to the slow unsupervised modification of connection weights. Based on the nonsmooth analysis techniques, we prove the existence and uniqueness of equilibrium for the system and establish some new theoretical conditions ensuring global exponential stability of the unique equilibrium of the neural network. Numerical simulations are conducted to illustrate the effectiveness of the derived conditions in characterizing stability regions of the neural network.

Dynamics of periodic delayed neural networks

This paper formulates and studies a model of periodic delayed neural networks. This model can well describe many practical architectures of delayed neural networks, which is generalization of some additive delayed neural networks such as delayed Hopfield neural networks and delayed cellular neural networks, under a time-varying environment, particularly when the network parameters and input stimuli are varied periodically with time. Without assuming the smoothness, monotonicity and boundedness of the activation functions, the two functional issues on neuronal dynamics of this periodic networks, i.e. the existence and global exponential stability of its periodic solutions, are investigated. Some explicit and conclusive results are established, which are natural extension and generalization of the corresponding results existing in the literature. Furthermore, some examples and simulations are presented to illustrate the practical nature of the new results.

Global dissipativity of continuous-time recurrent neural networks with time delay

This paper addresses the global dissipativity of a general class of continuous-time recurrent neural networks. First, the concepts of global dissipation and global exponential dissipation are defined and elaborated. Next, the sets of global dissipativity and global exponentially dissipativity are characterized using the parameters of recurrent neural network models. In particular, it is shown that the Hopfield network and cellular neural networks with or without time delays are dissipative systems.