The simplest mathematical models describing the spreading of information warfare are considered. New mathematical models which describe the process of information warfare are created. In particular, complete conditions are obtained for one of the participants to win in this warfare.Keywords: mathematical modeling, information security and warfare, communication between the members of a social community.

Mathematical models of information attack and information warfare in a society

The paper adds to the literature on propaganda wars. This area attracts practitioners as well as researchers from a variety of fields such as philosophy, social and political science, psychology. It also attracts IT researchers and mathematicians who develop and study models of propaganda wars. In this paper we apply the mathematical model of making choices by individuals to the problem of how the extent of social polarization affects the outcome of the propaganda battle. By the term "propaganda battle" we mean that each member of the society is subject to two competing flows of information. These two flows are generated by two competing parties and each flow consists of propaganda and rumor. That is each party runs propaganda via its own mass-media, and the rumor adds to propaganda as individuals get information from media and transmit it further through interpersonal communications with other individuals. The kind of society is considered which comprises two groups with diametrically opposite fundamental attitudes. The mathematical model has been investigated analytically and numerically. It is shown that moderate political polarization favors the side that runs more intensive propaganda. However, the advantage of stronger propaganda is impaired if the polarization is great enough, because neither media nor individuals can reassure their radical opponents.

The process of disseminating information in society among its possible adherents (individuals who perceive this information) under the conditions of «excitement» is considered, which means an increased level of interest in the assimilation of information. Moreover, the presence of excitement means that the influence on the rate of change of the current number of adherents, denoted N, consists of the influence not only of the media and the influence of interpersonal contacts between individuals depending on the value of N, but also the excitement and behavioral influence of adherents, , in addition, the rate of change of N over time. A corresponding mathematical model of this process is proposed and preliminary studied. The model has the form of an ordinary differential equation of the first order, not resolved with respect to the derivative. The areas of variation of the model parameters are determined for which the solution of the problem obviously exists. It is shown that under the restrictions on the parameters formulated in the work, the presence of excitement accelerates the process of society's perception of the proposed information, i.e. increases the rate of increase in the number of its followers.

The chapter discusses a number of mathematical models of information battle in techno-social environments. Some models take into account such battle factors as the mass information media's incomplete coverage of the society, the individuals' acquisition of the information only after receiving it twice, the individuals' forgetting the information, a priori bias to support a party to the battle, and polarization of the society. For simpler models, the results are described in brief. For more complicated ones, mathematical research has been conducted with the sociological interpretation of the results.