A Model of Information Warfare in a Society with a Piecewise Constant Function of the Destabilizing Impact

A model of information warfare in a society is considered that implies that individuals do not forget information and one of the parties periodically destabilizes the system using periodical short-time boost of the mass media broadcasting intensity. The model has the form of a system of two nonlinear ordinary differential equations with the periodic discontinuous right-hand side. The asymptotics of the first order with respect to a small parameter has been constructed, and a numerical example illustrating the qualitative behavior of the solution and the closeness of the constructed asymptotics to the exact solution has been provided.