In this paper, we consider the uniform asymptotic stability, global asymptotic stability and global exponential stability of the equilibrium point of discrete Hopfield neural networks with delays. Some new stability criteria for system are derived by using the Lyapunov functional method and the linear matrix inequality approach, for estimating the upper bound of Lyapunov functional derivative. ...

The chemical implementation of a neuron and connections among neurons described in prior work is used to construct collective neural networks. With stated approximations, these chemical networks are reduced to networks of the Hopfield type. Chemical networks approaching a stationary or equilibrium state provide a Liapunov function with the same extremal properties as Hopfield's energy function....

This paper surveys two advanced associative memory models[8][5]. The first model was derived from the projection on a closed convex set spanned by patterns. The second model was derived from training weights to improve the error tolerance of the Hopfield network. Both models are designed to resolve the insufficiencies of the Hopfield network. These insufficiencies are loading capacity, limit cy...

The convergence property for doing logic programming in Hopfield network can be accelerated by using new relaxation method. This paper shows that the performance of the Hopfield network can be improved by using a relaxation rate to control the energy relaxation process. The capacity and performance of these networks is tested by using computer simulations. It was proven by computer simulations ...

2014 We study pattern recognition in linear Hopfield type networks of N neurons where each neuron is connected to the z subsequent neurons such that the state of the ith neuron at time t + 1 is determined by the states of neurons i + 1, ...,i + z at time t. We find that for small values of z/N the retrieval behavior differs considerably from the behavior of diluted Hopfield networks. The maximu...

It is shown that a Hopfield neural network (with linear transfer functions) augmented by an additional feedforward layer can be used to compute the Moore-Penrose Generalized Inverse of a matrix. The resultant augmented linear Hopfield network can be used to solve an arbitrary set of linear equations or, alternatively, to solve a constrained least squares optimization problem. Applications in si...

J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Nat. Acad. Sci., USA, vol. 79, pp. 2254-2258, Apr. 1982. R. J. McEliece, et al., “The Capacity of the Hopfield Associative Memory,” IEEE Transactions on Information Theory, vol. T-33, pp. 461-482, 1987. B. L. Montgomery et al., “Evaluation of the use of Hopfield Neural Network Model as...

Abstract − The asymptotic behavior of a class discrete-time Hopfield neural network is studied in this paper. Some properties for this class discrete-time neural network, such as the boundedness of motion trajectory, the uniqueness and the absolute stability of equilibrium point etc, are obtained. In this paper, the sufficient conditions related to the existence of unique equilibrium point and ...

With the complexity increase in industrial production process, the traditional ProportionIntegration-Differentiation (PID) control can not meet the requirements of the control system performance. Because neural network has the ability of adaptive, self-learning and nonlinear function approximation, control equality of system is improved if it is combined with traditional PID. In the paper, Hopf...