Dynamical behavior of a neural network with periodical external inputs

Localized neural populations in different brain areas can undergo periodical external influence. To study this situation we consider the well known model by Wilson and Cowan (1972). It describes the evolution of two interconnected neuronal subpopulations of excitatory and inhibitory neurons correspondingly. Besides, it could be considered as a model of an abstract self-regulatory system. We describe and reveal underlying mechanisms of two regimes of forced oscillations in the model. In the first one the system acts as a phase comparator, demonstrating high sensitivity to a value of a phase shift between inputs to excitatory and inhibitory neurons. In the second regime it acts similar to a low pass filter: amplitudes of forced oscillations of the both components are not small and almost constant for low frequencies of the external input to the excitatory subpopulation. But they decrease significantly when the frequency becomes rather high. For simplified versions of the model analytical estimates for corresponding ranges of parameters are derived. It is shown that they are in good agreement with the results of computer simulations.