A bifurcation analysis of the four dimensional generalized Hopfield neural network

Abstract

Abstract A four neuron Hopfield neural network with asymmetric weights and self-connection is analyzed. Its stable steady state and periodic attractors are identified and a complete bifurcation diagram is constructed. A center manifold reduction is undertaken and by means of normal form theory, the characteristics of the limit cycles are obtained. The network is seen to have a large memory storage capacity with both fixed point and periodic memories coexisting. The onset of chaos as reported previously is considered.