Do All the Theoretical Results Obtained in the Case of Hopfield Neural Networks Have a Counterpart at the Level of the Human Neural System?

Continuous and discrete Hopfield type neural networks claim to be mathematical descriptions of electrical phenomena appearing in nervous system. We present a set of theoretical results having natural counterpart and another set of theoretical results concerning equilibriums that have no real counterpart at the level of the nervous system. The differentiation criterion of equilibriums is the local exponential asymptotic stability in Liapunov sense of the steady state voltage and the structural stability of the Hopfield system in Smale sense. The believe is that unstable equilibriums in Liapunov sense and equilibriums obtained in case of structurally unstable Hopfield systems, exist only in theory.