Universal Dynamical system for brain modeling

Abstract

In this paper, we propose a new model: infinite dimensional Lotka–Volterra–Hopfield (LVH) system, which is a combination of two celebrated models—the multispecies Lotka–Volterra system and the Hopfield model. We show that the LVH model enjoys a remarkable property: it serves as a dynamical analogue of universal Turing machine, generating all possible structurally stable dynamics by a variation of initial data. For a given number of neurons, this system has a larger associative memory than the traditional Hopfield and even modern Hopfield systems. The model has a new type of associative memory: it is capable to store entire dynamic systems. To illustrate new possibilities of the model proposed, some applications are considered, in particular, to pattern recognition.