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 time, the opposing parties are distributing Nt() and At the beginning the third party does not disseminate 1 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 JOURNAL OF CIRCUITS, SYSTEMS AND SIGNAL PROCESSING Volume 12, 2018 model does not directly focus on information streams, IV. COMBINED NONLINEAR MATHEMATICAL AND COMPUTER information receivers' - the number of informed personnel MODELS OF INFORMATION FLOW AND DISSEMINATION variability is essentially considered. In particular, the For the integrated mathematical models of the information following model is discussed: let's Nt() is a number of warfare, let's bring the relevant indications while taking into account the existing traditions. In particular, at informed potential customers about the object, N - the total 0 t ∈[0; +∞) moment, the number of information, distributed number of potential users, α1 ()t -intensity of advertising by each side is to be noted with Nt10 () , Nt20 () , Nt3 () . campaigns, α - advertising intensity by users, who know 2 ()t Quantity of information at moment t , it is calculated as the dN() t sum of the relevant party, the number of any provocative about the object , - the changing speed of users information, that is disseminated by all means of mass dt information. At the same time, the opposing parties are informed (adepts), which naturally depends on the number of uninformed consumers and the intensity of advertising reporting Nt10 () and Nt20 () number of information. The campaigns. That's why we get the mathematical model of the third - peaceful side calls on the sides to stop the information following kind of Samarskiy-Mikhailov: warfare, for which it disseminates Nt3 () number of dN() t =+−αα12()()()()t tNt() N 0 Nt . (2.1) information. Let's name Nt10 () , Nt20 () , Nt3 () the number dt Let's consider (2.1) substantiation of the model with more of "officially" disseminated information by the respective details. Advertising, as information is distributed in two ways: parties. Then model (1.3), (1.4) will be: first, directly through the advertising campaign, for example d Nt() Nt()()=αβ Nt1, −−10 Nt() via mass media, when by this way, increasing speed of the dt 10 1 10 I 1 3 informed population is proportionate to the number of 1 Nt uninformed population -α10()()t() N− Nt and second, an d 20 () Nt20 ()()=αβ2 Nt 20 1, −−2Nt 3 () (3.1) informed person about advertising tells his acquaintances dt I2 about this and thus become information spreaders, increasing speed of the informed population is proportionate to the d Nt3 () Nt3 ()()()=+−(γγ1 N 10 t 2 N 20 t)1. dt I3 number of uninformed population -α20()()t() N− Nt . In fact, advertising is spread by interpersonal relationships. When With initial conditions: we combine the speed of advertising spread in these two ways, NN10 ()0 = 10 , NN20 ()0 = 20 , NN3 ()0 = 30 . (3.2) we will get the model of the whole distribution speed of Let's say, the first side represents the population, which has advertising. In equation (2.1) starting point is, at the beginning maximum value of , in similar, the second side represents of the time, the number of advertised individuals is equal to xp zero: the population, which has maximum value of y p . xt1 () - the Nt() |0t=0 = (2.2) number of population of the first side, who at the time of One of the authors, A.P. Mikhailov, overtime, changed the t ∈[0; +∞) have "received" information officially reported name of (2.1) and (2.2) model's. At first in cooperation with academician A.A. Samarskiy, the monograph published in by the first party, became it's adept and by interconnected 1997 was called model of advertising campaign; then, since relationships themselves disseminate beneficial information for
2002 , it got called an information threat model [7]; since 2004 the first side by quantity of Nt11 () . xt2 () - the number of - information dissemination model [8]; since 2009, information confrontation model [6]; in 2011 - the model of information population of the first side, who at the time of t ∈[0; +∞) warfare [15]; in2015 - information attack and duel model [10], have "received" information officially reported by the second [17]. party, became it's adept and by interconnected relationships With model of (2.1), (2.2), A.P. Mikhailov and coauthors themselves disseminate beneficial information for the second create different models of dissemination of information, for side by quantity of Nt() . Similarly, we can do this for the example: model with forgetting the information, model of 12 information duel and others. population of the second party as well: yt1 () - the number of the population of the second party, which at the time of t ∈[0; +∞) has "received" information officially reported by the first party, became it's adept and by interconnected
ISSN: 1998-4464 222 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SIGNAL PROCESSING Volume 12, 2018 relationships themselves disseminate beneficial information for d Nt() Nt=α Nt1 −−10 the first side by quantity of Nt21 () . Also, yt2 () - the 10()() 1 10 dt I1 number of the population of the second party, which at the −β Nt(), time of t ∈[0; +∞) has "received" information officially 13 reported by the second side, became it's adept and by quantity d Nt20 () Nt20 ()()=α2 Nt 20 1 −− of Nt22 () . Speed of Nt11 () information dissemination, dt I2 −β Nt, naturally, depends on the meeting of the xt1 () adepts and the 23() population free of this information, particularly, d Nt3 ()()()=+×(γγ1 N 10 t 2 N 20 t) on xt11()()() xp − xt . In addition, if the adept spreads dt information without interpersonal communication, let's say Nt() ×−3 social network, or through the adepts own web means, then we 1, I3 should additionally consider the maximum capabilities of dx() t adept's I4 IT technologies. In addition, it is natural that the 1 =+×(αα3N 10()()() t 4 N 11 tx 1 t) "official" activity of the party, whose we consider, affects the dt adept activity. So, we have the following ratio: ×−()xp xt1 () , dN() t 11 =α −+ 11N 11 ()() t() xp xt1 xt 1 () dx2 () t dt (3.3) =+×(ααN()()() t N tx t) dt 5 20 6 12 2 +−α12N 10()() tI() 4 N 11 t. ×−()xp xt2 () , With initial conditions: N ()0= 0. (3.4) 11 dy() t 1 =+×αα In the same way we can make correlations for Nt() , ( 7N 10()()() t 8 N 21 tyt 1 ) 12 dt Nt21 () , Nt22 () , where we can note I5 , I6 , I7 , with ×−y yt() , ()p 1 maximum possibility of the information technologies of the dy2 () t adepts xt() , yt() , yt() . As for adepts xt() , =+×(αα9Nt 20()()() 10 Ntyt 22 2 ) 2 1 2 1 dt xt2 () , yt1 () , yt2 () , for them correlations are derived ×−()yp yt2 () , from Samarskiy-Mikhailov model, where an intensive dN() t advertising campaign is presented as α , where 11 ijNt0 () =α11N 11 ()() t() xp −+ xt1 xt 1 () dt = = i 3, 5, 7 , j 1, 2 , and the intensity of the dissemination of +−α12N 10()() tI() 4 Nt 11 , information by the adept is assessed as αkNt ls () , where dN() t k = 4,6,8,10 , ls,= 1, 2 . As a result we get the integrated 12 =α13N 12 ()() t() xp −+ xt2 xt 2 () mathematical model information warfare with restrictions: dt +−α N()() tI() N t, 14 20 5 12 dN21 () t =α15N 21 ()() t() yp −+ yt1 yt 1 () dt
+−α16N 10()() tI() 6 N 21 t, (3.5) dN() t 22 =α −+ 17N 22 ()() t() yp yt2 yt 2 () dt +−α 18NtINt 20()()() 7 22 . With initial conditions:
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N()()()0= nN , 0 = nN ,0 = n , words, let’s consider the simplest case of the model. For this, 10 10 20 20 3 30 for information flows we need to take the ignorance model of NNNN11, 12 , 21 , 22 = 0, (3.6) the enemy: = d xx1212()()()()0, 0, yy 0, 0 0. =αβ − Nt10()()() 1 Nt 10 1 Nt 3 , Thus, we have acquired an integrated mathematical model dt of information warfare with restrictions, which is described by d Nt()()()=αβ Nt − Nt, (4.1) the ordinary differential equation system (3.5), in which there dt 20 2 20 2 3 are eleven functional searches and eleven initial conditions (3.6). Note that in (3.5), (3.6) – Cauchy task, right side of (3.5) d Nt3()()()=γγ 1 N 10 t + 2 N 20 t. system have features and it dive us the basis to conclude that dt this Cauchy task has the one solution for the time With (3.2) initial conditions. In the model of Samarskiy- segment t ∈[0; +∞) . Mikhailov, let's represent a linear form for the activity of parties and adepts. In addition we are only considering Thus the number of useful information for the first party xt1 () , yt2 () adepts, who are only involved in correlations of Nt1 () is the sum of the “official” information of the first party, information of first side’s adepts in the first party disseminated information by Nt10 () , Nt20 () - sides. Let's population and information spread by adepts in the second say, that x1 ()() t= xt, y2 ()() t= yt. As a result we will party’s population which is beneficial for the first party – get an integrated mathematical model of information warfare, =++ NtNtNtNt1()()()() 10 11 21 . (3.7) which was formed at Sokhumi State University, faculty of And the number of useful information for the second party Mathematics and Computer Sciences, after discussion with Professor T. Chilachava and which has the form: - Nt2 () , represents the following sum: d NtNt2 ()()()()=++20 Nt 12 Nt 22 . (3.8) Nt10()()()()=α 1 Nt 10 +− νβ 1 xt1 Nt 3 , dt Third side impacts are clearly demonstrated in , Nt10 () d =α +− νβ Nt20 ()()()()2 Nt 20 2 yt2 Nt 3 , Ntinformation flows and by their means this impact is 20 () dt d realized in Nt, Nt, Nt, Ntflows. So, it is (4.2) 11 () 12 () 21 () 22 () Nt3()()()=γγ 1 N 10 t + 2 N 20 t, natural to raise the question – whether it is possible to put out dt information warfare with the activity of the third side, at any dx() t =+−()αγ33xt() () xp xt() , point in time, in different moments, Nt1 () , Nt2 () to dt become zero: dy() t ∗ ∗∗ =+−()αγ44yt() () yp yt() . Nt1 () = 0 , Nt2 () = 0 . (3.9) dt With initial conditions: Let’s call (3.5), (3.6), (3.9) boundary task the Chilker type task, because conditions for the right side are specific, in = = = particular, Nt, Nt functions cross zero generally in N10()()()0 nN 10 , 20 0 nN 20 ,0 3 n 30 , 1 () 2 () (4.3) different conditions and also these times are not fixed. In xy()()0= 0 = 0. model (3.5), (3.6), in the information flow, spread by adepts, If we say that, ααα= = , βββ= = , participating in the “official” information streams of opposing 12 12 sides. It not happens on the contrary, but it is possible. That’s γγγ12= = , ααδ34= = , ννν12= = . why it’s natural, in speed correlations of information spread by Then (4.2) will get the form: the adepts Nt11 () , Nt12 () , Nt21 () , Nt22 () were involved Nt() , Nt() of information streams. This case in 10 20 considered other models.
V. COMBINED MATHEMATICAL AND COMPUTER MODELS OF THE INFORMATION WARFARE FOR IGNORING OPPONENT Let’s consider the model task of Integrated mathematical and computer models of the Information Warfare, in other
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d and we will conduct a computer experiments. Let's say that we Nt()()()()=α Nt +− νβ xt Nt, have initial conditions: dt 10 10 3 NN()()()0= 0.1, 0 = 0.001, N 0= 3, d 10 20 3 Nt=α Nt +− νβ yt Nt, (4.10) 20 ()()()()20 3 xy()()0= 0 = 0. dt d Possibility of solving Chilker type (4.7)-(4.7) task, (4.4) Nt3 ()()()=γγ N10 t + N20 t, according to computer experiments, depends on the dt 2 aggressiveness of sides, in particular on D =α −8 βγ . For dx() t =+−()δµxt() () xp xt() , example, if the aggression of antagonistic sides is large, which dt cause D to be nonnegative: D ≥ 0 , then there is no solution dy() t to the Chilker type problem, which means that the third side =+−()δµyt() () yp yt() . dt cannot stop the information warfare by its actions. For Initial conditions are given in (4.3). There are five example, if α =1, 8 ; β = 0,05 ; ν = 0,05 ; γ = 0,05 ; unknown functions in the system (4.4), but the last two δ = 0,3 ; µ = 0, 2 ; xp =155 ; y p =150 ; which means equations of this system, which results from Samarskiy- that = , as we see on Figure 1_a, both antagonist Mikhailov model, will be analytically solved, when the D 3, 04 equation in the second string of (4.3) is completed for the forces strengthen the information warfare and third party's initial conditions, as a result we have: impact on them is unsuccessful. In the conditions of high aggression by the parties, if D = 0 , what happens for this δxexp δµ+− xt 1 pp()() meaning of parameters: α = 0,08 ; β = 0,08 ; ν = 0,05 ; xt() = , (4.5) δ δµ++ µ exp()()xtpp x γ =1; δ = 0,3 ; µ = 0, 2 ; xp =155 ; y p =150 ; then it is possible for one side to go to zero and third party can δyexp δµ+− yt 1 pp()() influence one of the antagonistic sides. See Figure 1_b. yt = , (4.6) 37 () x 10 inf warfare δexp δµ++yt µ y ()()pp 20 n1 By adding (4.4) into two equations, (4.5) and (4.6), we get n2 a system with tree equations: 15 n3 x d =α +− νβ y Nt10 ()()()() Nt10 xt Nt3 , 10 dt n1 n2 d 5 Nt20 ()()()()=α Nt20 +− νβ yt Nt3 , (4.7) n3 dt amount of information d 0 Nt3 ()()()=γγ N10 t + N20 t. dt x y
with initial conditions: 47.5 48 48.5 49 49.5 Time = = = (4.8) N10()()()0 nN 10 , 20 0 nN 20 ,0 3 n 30 , Figure 1_a. The parties involved in the IW, when D > 0 Notice, that it is possible to find analytical solutions of the 16 Cauchy task, because with transformations in (4.7) we will get x 10 inf warfare a linear no homogeneous ordinary differential equation of the 4 n1 n2 3 second order with constant coefficients towards Nt() , and n3 3 n1 2 x placing the solution system (4.7) - homogeneous ordinary y differential equation of first order with constant coefficient 1 0 towards Nt10 () , Nt20 () . But after adding the Cauchy task -1 n3
(4.7), (4.8) conditions to the right end: amount of information ∗ ∗∗ -2 y n2 Nt10 () = 0 , Nt20 () = 0 . (4.9) x -3 ∗ ∗∗ Where t , t are non-fixed, in general, different time 20 25 30 35 40 45 50 55 60 65 Time moments on time []0,T > 0 period, we will get a Chilker Figure 1_b. The parties involved in the IW, when D = 0 type task, which we will investigate via computer modeling
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As for the case of low aggression, when D < 0 , in The computer experiment was also conducted (4.7)-(4.7) in particular for parameters: α = 0,08 ; β = 0,5 ; ν = 0,05 ; the general case of the Chilker type problem. In particular, when the antagonistic parties have different aggressiveness γ =1; δ = 0,3 ; µ = 0, 2 ; xp =155 ; y p =150 ; then ()αα12, and peace readiness ()ββ12, indicators, also third party impacts are effective on antagonistic sides, they go to zero, which means that the Chilker type problem has a different values of peacekeeping activity towards the parties solution. ()γγγ123,, , in the equations of adept's quantity the number Based on analysis of results of computer experiments, we of information streams of relevant opposing parties is can conclude, that solution behavior of integrated included: mathematical model of ignoring the enemy is similar to d relevant non integrated mathematical model solutions [16], =α +− νβ Nt10()()()() 1 Nt 10 1 xt1 Nt 3 , [17], in particular, dependence of solutions on D -on the level dt of aggressiveness of parties. At the same time, it should be d Nt()()()()=α Nt +− νβ yt Nt, noted that the number of adepts in the model has made some dt 20 2 20 2 2 3 corrections, for example, under conditions of low aggression, d D is negative and increases in module, then for little time Nt3()()()()=++γγ 1 N 10 t 2 N 20 tγ 3 Nt 3 , (4.11) value the antagonistic side for parameters α = 0,08 ; dt β =15 ; ν = 0,05 ; γ = 3, 5 ; δ = 0,3 ; µ = 0, 2 ; dx() t =+−(αγ3N 10()() t 4 xt)() xp xt() , dt xp =155 ; y p =150 , D = −419,9 , go to zero, see Figure 2_a. but, for big t , one of the antagonistic sides (depends on dy() t =+−(αγ4N 20()() t 5 yt)() yp yt() . correlations of the initial values of the parties) doesn't go to dt zero, see Figure 2_b. The computer experiment was conducted for the system inf warfare (4.11) with different initial conditions (4.10) and parameters. 3 n1 We can conclude from the results obtained, that the relevant n2 2.5 x,y n3 Chilker type task - (4.11), (4.6), (4.9) has a solution, in case of x 2 n3 y nigh peace readiness and activity. In particular, if we have the n1 1.5 data of parameters, where aggressiveness prevails over peace
1 readiness and activity: α1 = 4,8 ; β1 =,5; ν1 =1, 5 ; 0.5 α = 5, 6 ; β =,7; γ =,05 ; γ =,3; γ =,07 ; 0 2 2 1 2 3 amount of information
-0.5 xp =155 ; y p =150 ;α3 = 2,3 ; α4 = 2, 2 ; γ 4 =,2; -1 γ = n2 5 ,3, then the antagonistic parties develop information -1.5
0 0.5 1 1.5 2 warfare and the third party's impact is unsuccessful, see Figure Time 3_a, which is derived for initial conditions - Figure 2_a. The parties involved in the IW, when D < 0 NN10 ()()()0= 0.2,20 0 = 0.01, N3 0 = .03, (4.12) = = inf warfare xy()()0 0 0. 200 n1 The Chilker type problem (4.11), (4.6), (4.9) has a n2 solution when the aggressiveness of opposing parties is 150 n3 x relatively low, for example, for parameters: α1 =,08 ; y x 100 y β1 =1, 5 ; ν1 =,05 ; α2 =,06 ; β2 =1, 7 ; γ1 =,05 ; n1 50 γ 2 =,03 ; γ 3 =,07 ; xp =155 ; y p =150 ;α3 =,3; 0 α =,2; γ =,2; γ =,3, see Figure 3_b.
amount of information 4 4 5
-50 n3 n2
5 10 15 20 25 30 35 40 45 50 Time Figure 2_b. The parties involved in the IW, when D < 0
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inf warfare faculty of applied mathematics and computer science,
250 n1 Professor in direction of mathematical modeling T. n2 n3 Chilachava, for held discussion about information warfare's x 200 x integrated models and useful advices, which significantly y helped research in the direction. 150 I express my gratitude to the Shota Rustaveli National Science Foundation of Georgia, for financial support in y 100 preparing the article through the grant YS17_78
amount of information n1 50 n2 n3 REFERENCES [1] Kereselidze N. Mathematical modeling of information warfare. 0 Monogram. (In Georgian). National Parliamentary Library of Georgia
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 ISBN: 978-9941-0-4892-0. 2012 year 176 p. Time http://kereseli.besaba.com/monografia%20formatizaziiT.pdf. Figure 3_a. The parties involved in the IW for Chilker type [2] Chilachava T., Kereselidze N. Mathematical Model of Information Warfare. (In Georgian). Georgian Electronic Scientific Journal: task - (4.11), (4.12), (4.9), with high aggression Computer Science and Telecommunications. 2010, no. 1 (24). p. 78 - 105. inf warfare [3] Chilachava T., Kereselidze N. About one mathematical model of the information warfare. Fifth congress of mathematicians of Georgia. 3 n1 n2 Abstracts of contributed talks. Batumi/Kutaisi, 9-12 October. 2009. p. 2 n3 85. n3 x [4] Chilachava T., Kereselidze N. Non-preventive continuous linear y 1 mathematical model of information warfare. Sokhumi State University Proceedings, Mathematics and Computer Sciences vol. 7. 2009, № 7. p. 0 91 – 112.. n1,n2 -1 [5] Chilachava T., Kereselidze N. Continuous linear mathematical model of preventive information warfare. Sokhumi State University
amount of information -2 Proceedings, Mathematics and Computer Sciences vol. 7. 2009, № 7. p. y x 113 – 141.. -3 [6] Kereselidze N. Mathematical model of information warfare taking into
-4 account the capabilities of the information technologies of the opposing sides. (In Russian). Transactions II The International Technical
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Conference dedicated to the 90th anniversary of the Georgian Technical Time University "Basic Paradigms in Science and Technology", 21st Century, Figure 3_b. The parties involved in the IW for Chilker type Tbilisi, Georgia, September 19-21, 2012. Publishing House "Technical task - (4.11), (4.12), (4.9), with low aggression University", Tbilisi, 2012, p. 188-190. [7] Kereselidze N. Mathematical model of information confrontation taking Computer experiments were conducted in the Mat Lab into account the possibilities of Information Technologies of the parties. (In Russian). // Proceedings of the XX International Conference environment, m-file were created Problems of Security Management of Complex Systems. Moscow, December 2012, art. 175-178. [8] Kereselidze N. Mathematical and computer models of information VI. CONCLUSION warfare. Monograph. (In Georgian). ISBN 978-9941-0-9617-4 (PDF). 2017. In the present work there is offered integrated http://kereseli.besaba.com/Math_and_comp_models_IW_monograph_2 mathematical and computer models of information warfare 017.pdf. in which independently expressed approaches till now are [9] Chilachava T., Chakhvadze A. Continuous Nonlinear mathematical and computer model of information warfare with participation of interstate reflected. In particular, academician A.A. Samarskiy and authoritative institutes. Georgian Electronic Scientific Journal: his coauthor's, Professor A.P. Mikhailov's advertising Computer Science and Telecommunications 2014| No. 4(44), p. 53 – campaign and professor T. Chilachava's tree sides 74. information stream (flow) models are united. It provides [10] Chilachava T., Chakhvadze A. Non llinear Mathematical and Computer new general linear model of information warfare; model Models of Information Warfare with Participation of Autoritative with restrictions on information technologies, private and Interstate Institutes. Book of abstracts V Annual International Conference of the Georgian Mathematical Union, Batumi, September 8- advanced integrated mathematical and computer models of ignore enemy. For last two models, computer experiments 12, 2014. p. 76. [11] Samarskiy AA, Mikhailov AP Mathematical modeling: Ideas. Methods. have been conducted, which helped to identify solving Examples. 2nd ed. Correction. - M. FIZMATLIT. 2005. 320 pp. possibility of Chilker type task for information warfare. [12] Marevtseva N.A. Mathematical models of information attack and information confrontation. Jour. Sociology. No. 3. 2011 p. 26 -35.. VII. ACKNOWLEDGMENT [13] Mikhailov A.P., Izmodenova K.V. On optimal control in the I would to thank the Vice-President of the Academy of mathematical model of information dissemination. (In Russian). Sciences of Tskhum-Abkhazia, Sukhumi State university's
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Proceedings of the seminar "Mathematical modeling of social processes", compilation, issue. 6. - Moscow: MAX Press, 2004. [14] Marevtseva N.A. The simplest mathematical models of information confrontation. (In Russian). / Series "Mathematical Modeling and Modern Information Technologies", no. 8. // Collection of works of All- Russian scientific youth schools. Rostov-on-Don, the publishing house of the Southern Federal University. 2009. P. 354-363. [15] Mikhailov A.P., Marevtseva N.A. Models of information struggle. (In Russian). // Math modeling. 2011. P. 23. № 10. P. 19-32. [16] Mikhailov A.P., Petrov A.P., Proncheva O.G., Marevtseva N.A. Mathematical modeling of information confrontation in society. (In Russian). International Economic Symposium 2015. Materials of the International scientific conferences devoted to the 75th anniversary of the Faculty of Economics of the St. Petersburg State University: a collection of articles. Sheaf Ed. S.A. Belozerov, OOO "Scythia-print", St. Petersburg, 2015. S. 293-303. URL: http://econ- conf.spbu.ru/files/Symposium_Sbornik_Statey.pdf. [17] Mikhailov A.P., Petrov A.P., Proncheva O.G., Marevtseva N.A. Mathematical Modeling of Information Warfare in a Society // Mediterranean Journal of Social Sciences. Vol. 6. No. 5 S2. pp. 27–35.
Nugzar Kereselidze - was born in Tbilisi, Georgia on January 31, 1955. In 1977 graduated from the Faculty of Cybernetics and Applied Mathematics of the Tbilisi State University, Georgia. Defended doctoral dissertation at the Georgian University named after Andrew the First-Called, and became the academic doctor of Informatics. Since 2013, he is assistant professor of the Sukhumi State University. 1977-1983 he was the research associate of Institute of Cybernetics of Academy of Sciences of Georgia. 1983-2006 lecturer of the Abkhazian State University and Sukhumi branch of the Tbilisi State University. N. Kereselidze, An Optimal Control Problem in Mathematical and Computer Models of the Information Warfare. Differential and Difference Equations with Applications : ICDDEA, Amadora, Portugal, May 2015, Selected Contributions. /Editors: Pinelas, S., Došlб, Z., Došlэ, O., Kloeden, P.E. (Eds.), Springer Proceedings in Mathematics & Statistics, 164, DOI 10.1007/978-3-319-32857-7_28, Springer International Publishing Switzerland 2016 http://www.springer.com/gp/book/9783319328553, 2016, p. 303-311. N. Kereselidze, Optimizing Problem of the Mathematical Model of Preventive Information Warfare. Informational and Communication Technologies – Theory and Practice: Proceedings of the Inter national Scientific Conference ICTMC-2010 USA, Imprint: Nova https://www.novapublishers.com/catalog/product_info.php?products_id=2 5352, 2011, p. 525-529. Dr. Nugzar Kereselidze, member of the Georgian Mathematical Union - GMU, member of presidium of the GMU.
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