Stochastic high-order hopfield neural networks

Authors:
Yi Shen;Guoying Zhao;Minghui Jiang;Shigeng Hu
Affiliations:
Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, China;Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, China;Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, China;Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei, China
Venue:
ICNC'05 Proceedings of the First international conference on Advances in Natural Computation - Volume Part I
Year:
2005

Citing 5
Cited 4

Self-organising continuous attractor networks with multiple activity packets, and the representation of space

Neural Networks
Exponential Periodicity of Continuous-time and Discrete-Time Neural Networks with Delays

Neural Processing Letters
On Robust Exponential Periodicity of Interval Neural Networks with Delays

Neural Processing Letters
High-Order hopfield neural networks

ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
High-order neural network structures for identification of dynamical systems

IEEE Transactions on Neural Networks

Robust h∞ control for delayed nonlinear systems based on standard neural network models

ISNN'06 Proceedings of the Third international conference on Advnaces in Neural Networks - Volume Part II
Stability analysis of neutral neural networks with time delay

ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
Robust stability analysis of uncertain hopfield neural networks with markov switching

ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
Numerical analysis of a chaotic delay recurrent neural network with four neurons

ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I

Quantified Score

Hi-index	0.00

Visualization

Abstract

In 1984 Hopfield showed that the time evolution of a symmetric Hopfield neural networks are a motion in state space that seeks out minima in the energy function (i.e., equilibrium point set of Hopfield neural networks). Because high-order Hopfield neural networks have more extensive applications than Hopfield neural networks, and have been discussed on the convergence of the networks. In practice, a neural network is often subject to environmental noise. It is therefore useful and interesting to find out whether the high-order neural network system still approacher some limit set under stochastic perturbation. In this paper, we will give a number of useful bounds for the noise intensity under which the stochastic high-order neural network will approach its limit set. Our result cancels the requirement of symmetry of the connection weight matrix and includes the classic result on Hopfield neural networks, which is a special case of stochastic high-order Hopfield neural networks. In the end, A example is given to verify the effective of our results.