Equivalence of conventional and modified network of generalized neural elements

The article is devoted to the analysis of neural networks consisting of generalized neural elements. The first part of the article proposes a new neural network model — a modified network of generalized neural elements (MGNE-network). This network developes the model of generalized neural element, whose formal description contains some flaws. In the model of the MGNE-network these drawbacks are overcome. A neural network is introduced all at once, without preliminary description of the model of a single neural element and method of such elements interaction. The description of neural network mathematical model is simplified and makes it relatively easy to construct on its basis a simulation model to conduct numerical experiments. The model of the MGNE-network is universal, uniting properties of networks consisting of neurons-oscillators and neurons-detectors. In the second part of the article we prove the equivalence of the dynamics of the two considered neural networks: the network, consisting of classical generalized neural elements, and MGNE-network. We introduce the definition of equivalence in the functioning of the generalized neural element and the MGNE-network consisting of a single element. Then we introduce the definition of the equivalence of the dynamics of the two neural networks in general. It is determined the correlation of different parameters of the two considered neural network models. We discuss the issue of matching the initial conditions of the two considered neural network models. We prove the theorem about the equivalence of the dynamics of the two considered neural networks. This theorem allows us to apply all previously obtained results for the networks, consisting of classical generalized neural elements, to the MGNE-network.