Modeling of neural systems and networks by functional differential equations

The article considers models of neural systems in the form of functional differential equations, models with distributed delay, obtained by generalizing their corresponding systems with discrete delay, described by differential-difference equations. It is shown that such a generalization allows, while preserving all the capabilities of models with discrete delay in terms of simulating self-oscillations characteristic of neural networks, to give the latter a more adequate character. This is confirmed by the results of modeling the Hutchinson system with distributed delay using Matlab tools, which showed the presence of a period and the nature of self-oscillations depending on the model parameters and, therefore, the feasibility of burst and single transmission of nerve impulses. The capabilities of systems with distributed delay in the feedback circuit due to the multiple propagation paths of disturbances both in the interneuron medium and in the network connections are shown. During the simulation, the distribution of delay approximated by a second-order polynomial in a system of independent exponential functions is considered.