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, the paper will discuss the convergence of high-order Hopfield neural networks. The obtained results ensure that high-order Hopfield neural networks ultimately converge to the equilibrium point 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 high-order Hopfield neural networks. In the end, A example is given to verify the effective of our results.
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