A model of information warfare in a society with a piecewise constant periodic function of desstabilizing impact

The model of information warfare in society is considered in the absence of forgetting information by individuals in the case when one of the parties periodically destabilizes the system by means of a short-term jump in the increase in the intensity of broadcasting of the mass media. The model has the form of a system of two nonlinear ordinary differential equations with periodic discontinuous right-hand side. The asymptotics of the first order in a small parameter is constructed, a numerical example illustrating the qualitative behavior of the solution and the closeness of the constructed asymptotics to the exact solution is given.