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Combined Continuous Nonlinear Mathematical and Computer Models of the Information Warfare

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Combined Continuous Nonlinear Mathematical and Computer Models of the Information Warfare INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SIGNAL PROCESSING Volume 12, 2018 Combined continuous nonlinear mathematical and computer models of the Information Warfare Nugzar Kereselidze quite productive and successfully implemented in different Abstract - In this paper, the first attempt is made to combine countries of the world. A number of mathematical and existing approaches of mathematical and computer modeling of computer models have been developed, which takes into information warfare. As a result, integration mathematical and account the course of information war in the conditions of computer models of information warfare were created. Until now, in different regimes: Restriction of information, continuity, the mathematical modeling of the information warfare, issues of information flows and information dissemination were considered discretion, and more. The models are basically two studying separately. The first direction was initiated by the idea of Professor T. objects. First, the information itself, which is distributed as a Chilachava, to study the distribution of information flows of the two stream and is intended to discredit the opposing side. Second - opposite and third peacekeeping sides by mathematical models. The the number of people who have received the information second direction was laid by Academician A.A. Samarskiy and disseminated by the side. It is noteworthy that the models Professor A.P. Mikhailov, who proposed a mathematical model for developed so far have mostly discussed only the number of the dissemination of information among the population. Both these directions have been intensively developed and many scientific information flows or the number of people who have received studies have been devoted to them. Several dozens of interesting the information. In the presented work, an attempt is proposed models were created, which reflect the various nuances of the to unify these two approaches, which results in new types of problem. But it is natural that the information and the information for mathematical and computer models. Before representing the which it is intended should be studied together. During the results of combining these two traditional methods together, implementation of this idea, integrated mathematical and computer models of information warfare were created. Integrated common let’s talk about them separately. linear and nonlinear mathematical and computer models of information warfare were created. In this paper, integrated general II. MATHEMATICAL MODELS OF FLOW OF THE INFORMATION and particular mathematical and computer models for ignoring the WARFARE enemy are presented. With the help of computer research, a numerical experiment, the question of the existence of a solution to The mathematical modeling of the streams in the the problem of the Chilker range is studied, which is equivalent to the information war starts from year 2009, when Georgian task of completing information warfare. scientist Temur Chilachava’s original idea was worked out and reported in the same year on the fifth congress of Georgian Keywords— information warfare, integration mathematical Mathematicians [14] and it was published in Sokhumi State model, integration computer model, Chilker type task. University works [15],[ 16]. We will bring you a general linear model, as well as a nonlinear model with restrictions. Let’s I. INTRODUCTION consider the mathematical and computer models of mong the diverse types of information warfare, we are information warfare, in which the search size is considered as A attracted to the confrontation of the opponents in the the number of provocative information spread by two information field: when the sides use, for example, mass antagonists and the number of peacekeeping calls made by the dissemination of information and with it try to misinform the third, peacekeeper side. All three parties involved in the enemy, compromise them, etc. The objectives and means of information warfare spread information of the relevant party, information warfare in this direction are detailed in the works and any number of promotional information to achieve its [1], [3]. This type of information war can be called goal. At the moment of time t ∈0; +∞ the number of information confrontation, but for simplicity we will use [ ) “information warfare” for this type of information warfare. information disseminated by each party should be noted as Mathematical methods of studying information warfare are Nt1 (), Nt2 (), Nt3 () . Quantity of information at the moment of time is calculated as the sum of the relevant This work was supported by Shota Rustaveli National Science Foundation t of Georgia (SRNSFG) under Grant № YS17_78. party, the number of any provocative information that is Nugzar Kereselidze is with the Department of Mathematics and Computer distributed by all means of mass information. At the same Science, Sukhumi State University, Tbilisi, Georgia, (phone: 995 577 963 923; e-mail: [email protected]). ISSN: 1998-4464 220 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SIGNAL PROCESSING Volume 12, 2018 At the beginning the third party does not disseminate time, the opposing parties are distributing Nt1 () and information ( N30 = 0 ) or make preventative conciliatory Nt2 () numbers of information. Third, the Peaceful Party statements ( N30 > 0 ). Peacekeeping side then begins to react calls on the parties to stop the information war, for which the to the provocative information spread by the parties. For the peacekeeper spreads relevant information. As the opposing first time mathematical and computer models of information side aims to influence the information impact on his rival, he warfare, taking into consideration the possibilities of IT tries to disseminate as much as discreditable information as technologies, It was proposed in 2012 [4], [5], and was possible about the opponent. At the same time, the generalized later [2]: dissemination of previously used information is allowed and new disinformation is added. Thus, the speed of dissemination d xt() xt()()=αβ xt 1, −−zt() of information by the opposing party depends on the number 11 dt I1 dN1 () t of information already distributed: α11Nt() , d yt() dt yt()()=αβ22 yt1, −−zt() (1.3) dt I2 dN2 () t β . In addition, the opposing side reacts 22Nt() d zt() dt zt()()()=+−(γγ xt y t)1. 1 22 to the number of information disseminated by the rival and the dt I3 peacekeeping parties. Thus, the speed of dissemination of ()0 = xx , ()0 = yy , ()0 = zz . (1.4) information by the opposing party depends also on: 0 0 0 dN() t dN() t Where xt() , yt() is the number of disseminated 1 (ααNt()()− Nt), 2 dt 22 33 dt information by the antagonistic sides at moment - t . Similarly, the peacekeeping - third side's disseminated amount of (ββ11Nt()()− 33 Nt) . Third, the intensity of information information zt() at the same t time. α , α accordingly is disseminated by the Peace Party depends not only on the 1 2 number of information disseminated by him, but also on how aggressive coefficients of the first and second opposing sides, aggressively the information warfare is going on, how much β1 , β2 - peaceful activity options for the opposing sides, γ1 , number of information is disseminated by opposing sides. γ - index of peacekeeping activity of the third party towards Taking into account these considerations, we can discuss 2 general linear continuous mathematical model of information the relevant opposing side. I j , j =1, 2, 3 - maximum number warfare: of technological capabilities of the first and second sides. dN t 1 () xt() , yt() , zt() functions are defined in the section =+−αα11Nt()()() 2 Nt 2 α 33 Nt, dt []0,T . dN2 () t =+−ββ11Nt()()() 2 Nt 2 β 33 Nt, (1.1) The opposing side reduces the speed of information dt dissemination according to how close is the number of dN3 () t information dissemination by him at the time to the maximum =++γγ11Nt()()() 2 Nt 2 γ 33 Nt, number of available of information dissemination. dt Besides mentioned mathematical models of information Initial conditions: warfare, continuous linear and discrete models of ignorance of the opponent have been developed; non-linear, continuous and N1 ()0= NN10 ,0 2 () = NN20 ,0 3 () = N30 . (1.2) linear discrete models taking into consideration authoritative Whereαα1323,,, β β≥ 0, γ i γ i ≥ 0 i =1, 3 ; αβ21, , -are organizations or institutions (Religious, non-governmental, constant sizes. Let’s name these constant sizes “Model ratios”. scientific, political and other) [12], [13]. The speed of change in the number of information disseminated by the first and second parties in the general linear model (1.1) depends on the number of information III. MATHEMATICAL MODELS OF DISSEMINATION INFORMATION FLOW disseminated by the parties and the international peace organization. Third - the speed of change of the number of The mathematical model of dissemination of information calmative information released by international organizations discussed in the classical work of mathematical modeling by is linearly increasing and is directly proportionate to the A.A. Samarskiy and A.P. Mikhailov [11]. The mathematical number of information disseminated by all three parties. In the model of organizing advertising campaigns is offered, based initial (1.2) conditions, N , N , N are non-negative on the principle of model universality, can be used in 10 20 30 mathematical modeling of information warfare. However, this permanent sizes. ISSN: 1998-4464 221 INTERNATIONAL
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