The Limited Solutions Method for Telecommunications Network Information Security Models

Abstract

Processes with instantaneous (abrupt) changes are observed in radio engineering (pulse generation), in biology (heart work, cell division, signal transmission by neurons), in control theory (work of industrial robots), in social systems (social communications, information dissemination). Therefore, the qualitative study of impulse systems in this work is an urgent task in modern theory of mathematical modeling.The work is devoted to the study of the existence of bounded solutions along the entire real axis (on the half-axis) of weakly nonlinear systems of differential equations with impulsive perturbations at fixed moments of time. The notion of a regular and weakly regular system of equations for the class of weakly nonlinear impulse systems of differential equations is introduced.Sufficient conditions for the existence of a bounded solution for an inhomogeneous system of differential equations in the case of weak regularity of the corresponding homogeneous system of equations are obtained. The conditions for the existence of the unique bounded solution on the whole axis for weakly nonlinear impulse systems are established. The obtained results are applied to the study of bounded solutions of impulsive SIR model that can be considered as a model which describes the dissemination of information on social networks.