Symbiosis of an artificial neural network and models of biological neurons: training and testing

In this paper we show the possibility of creating and identifying the features of an artificial neural network (ANN) which consists of mathematical models of biological neurons. The FitzHugh--Nagumo (FHN) system is used as an example of model demonstrating simplified neuron activity. First, in order to reveal how biological neurons can be embedded within an ANN, we train the ANN with nonlinear neurons to solve a a basic image recognition problem with MNIST database; and next, we describe how FHN systems can be introduced into this trained ANN. After all, we show that an ANN with FHN systems inside can be successfully trained and its accuracy becomes larger. What has been done above opens up great opportunities in terms of the direction of analog neural networks, in which artificial neurons can be replaced by biological ones. \end{abstract}