Neural Flows in Hopfield Network Approach

Abstract In most of the applications involving neural networks, the main problem consists in finding an optimal procedure to reduce the real neuron to simpler models which still express the biological complexity but allow highlighting the main characteristics of the system. We effectively investigate a simple reduction procedure which leads from complex models of Hodgkin-Huxley type to very convenient binary models of Hopfield type. The reduction will allow to describe the neuron interconnections in a quite large network and to obtain information concerning its symmetry and stability. Both cases, on homogeneous voltage across the membrane and inhomogeneous voltage along the axon will be tackled out. Few numerical simulations of the neural flow based on the cable-equation will be also presented.