Dynamic analysis of unstable Hopfield networks

In this paper, the dynamic behaviors of unstable Hopfield neural networks (HNNs) with asymmetric connections are studied. It is found that the solution of the HNN is bounded and the HNN is a dissipative system. In addition, sufficient conditions for the instability of the equilibrium point and the existence of stable limit cycles are proposed. Some numerical simulations are given to illustrate the effectiveness of the proposed results. It is shown that some HNNs exhibit two independent limit cycles or chaotic attractors which are symmetric to each other with respect to the origin.