Representation of Hopfield´s biological neural network via particle dynamics considerations

Within the framework of depicting the neuronal assembly as a system of interconnected cells, the activities associated with the neurons are viewed, in general, as a collective stochastical process characterized by a random proliferation of state-transitions across the interconnected units. This progression of state-transitions across a neuronal assembly, where each cell is characterized randomly by a dichotomous potential state, corresponds to a ´collective movement´ process. Such a stochastical process is modeled presently as a particulate motion in a disordered system with the dual characterization of a wave as well. Hence, considered are particle dynamics aspects of the neuronal collective movement of the state-transitional process.