Identifying the Transition of Interactions in Virtual Communities of Social Networking Services to Chaotic Dynamics Kateryna Molodetska1, Serhiy Veretiuk2 and Volodymyr Pilinsky3 1,2 Polissia National University, 7, Blvd. Stary, Zhytomyr, 10008, Ukraine 3 National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, 37, Prosp. Peremohy, Kyiv, 03056, Ukraine Abstract The diversification of communication channels influenced by the development of information and communication technologies has made social networking services particularly popular among users. They provide actors with many tools not only for effective communication and networking in virtual communities but also for self-organization and coordination of interactions in real life. As a result of the diffusion of boundaries in the information space, social networking services have become an object of threats to the information security of the state. The experience of information operations against information security of the state has shown that because of targeted information impact on virtual communities of actors can occur chaotization of processes of their interaction. The result of such impact is a transition of such processes from online to real life in the form of mass civil protests. With the constant growth in the number of threats and the emergence of new methods of destructive information impact, the problem of their early detection and effective counteraction becomes particularly important. It is known that the transition of virtual community to deterministic chaos is characterized by increasing levels of entropy in the system. In this article, we use the kernel density estimation of the entropy distribution of the actors' interaction parameters in the social networking services to determine its dynamics to identify growth periods, preceding the system's transition to chaotic dynamics. Determination of the nature of entropy function's variation from time will make it possible to determine the moments of application of controlling influence on information space of the social networking services and actors, which will ensure reduction of the system's degrees of freedom with its subsequent transition to a given state of information security. In this state the structure of virtual communities’ changes because of the self- organization of actors, providing information exchange in communities, which is resistant to destructive impact. Application of the proposed approach will improve the effectiveness of countering threats to state information security in the social networking services. Keywords 1 Social networking services, chaotic dynamics, kernel density estimation, entropy, Rössler attractor 1. Introduction communication [1-5]. Under these conditions, social networking services have become not only a leading source of information due to a high The growing influence of social networking degree of trust in the content of the services but services on social communication processes has also an instrument of covert influence on social turned them into a leading channel of III International Scientific And Practical Conference “Information Security And Information Technologies”, September 13–19, 2021, Odesa, Ukraine EMAIL: kateryna.molodetska@polissiauniver.edu.ua (A. 1); sergey.veretiuk@gmail.com (A. 2); pww@ukr.net (A. 3) ORCID: 0000-0001-9864-2463 (A. 1); 0000-0002-7915-9991 (A. 2); 0000-0002-2569-9503 (A. 3) ©️ 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). CEUR Workshop Proceedings (CEUR-WS.org) and political processes in the state [6-8]. Threats information security in the social networking to information security of the state in social services [11, 15, 16]. networking services of a communicative nature The purpose of the article is to determine a are connected to the realization of the needs of point in time for effective implementation of the individuals, society and the state for the creation, control action, followed by the transition of virtual consumption, dissemination, and development of communities of actors in the social networking national strategic content. Threats in social services from chaotic interaction with a given networking services may be aimed at influencing state, in which the levelling of destructive the mental and emotional state of actors, information influence the actors is ensured. influencing their freedom of choice, calling for To achieve the goal, the following tasks are separatism, the overthrow of constitutional order, required: violation of territorial integrity, discrediting state 1) Formalize the interaction of actors in virtual authorities, supporting, accompanying, or communities of social networking services under activating criminal or terrorist activity, etc. [9, the influence of threats using irregular attractors. 10]. In the conditions of globalization of the 2) Estimate system entropy using kernel national information space, absence of state density estimation of actor interaction parameters borders in virtual information environment, in social networking services. constantly growing number of threats to 3) Identify existing precursors of chaotic information security of the state, the problem of dynamics of actors' interaction in the social modelling actors' interaction in virtual social networking services and give practical networking services communities becomes recommendations for their early identification. especially topical. Research into processes of interaction between actors in the information 2. Modelling actors’ interaction in space of the social networking services, considering the influence of threats, will make it social networking services based possible to systematically counteract destructive on irregular attractors information influence, which remains uncontrollable [11, 12]. In the case of transition of social networking Analysis of recent research and publications services actors' interaction to deterministic chaos, [13-15] has shown that one of the promising it is characterized by the high sensitivity of virtual approaches to modelling social networking communities to changes in system parameters and services as a class of complex dynamic systems is the action of disturbances, in particular dynamic chaos theory. It allows considering key destructive information influences. Even if the properties of social networking services – high interaction of actors in the social networking sensitivity to initial conditions, as well as services is formalized by deterministic models, in openness, nonlinearity, non-equilibrium and a state of deterministic chaos, their dissipativity of interaction in virtual communities. communication turns into random and When interaction in social networking services unpredictable processes (Figure 1). turns to chaotic dynamics under the influence of information operations, not only the prediction of such interaction of actors becomes impossible, but also the system's behavior itself changes uncontrollably. Such behavioral features can occur not only in the virtual space of the social networking services but can also be reflected in the actions of citizens in real life. Therefore, within the framework of Figure 1: Social networking services as a target of solving the problem of modelling actors' threats interaction in virtual communities of services, not only the synthesis of control actions but also the To describe the interaction of actors in the point in time at which such a measure is social networking services when the system implemented, is of particular importance. This transitions to chaotic dynamics, it is advisable to approach will make it possible to suppress chaotic use irregular attractors. Even though social dynamics of interaction and form prerequisites for networking services is a dissipative system, which effective counteraction to threats to state can be either open or non-equilibrium, using the information resistance to destructive information irregular attractors is appropriate. influence; 𝑍(𝑡) is the function that determines the The features of irregular attractors are the actor's level of readiness for active actions in real complex geometric structure of the set of states of life, which is induced by destructive information the system they describe. Such attractors are influence 𝐼(𝑡), 𝑍(𝑡) > 0; 𝛾 is a parameter that characterized by a simultaneous combination of determines the level of destructive information both stability and instability. Therefore, irregular influence on actors aimed at overcoming their attractors provide a high degree of adequacy in information resilience and is related in inverse describing the interaction of actors in the social relation to 𝜃, 𝛾 < 0; 𝜃 is a parameter of actor's networking services, which are taking place under readiness level to move to active actions in real the conditions of information confrontation. Such life; 𝜉 is an information influence that is attractors include Lorenz attractors, Rössler performed using strategic communication attractors, and others [17, 18]. channels and is aimed at building information resilience in actors, 𝜉 > 0; 𝜇 is a parameter that 2.1. Rössler chaotic system determines the actors' prior experience in identifying threats in the social networking services; 𝑎 is an integrative parameter that In general terms, the actors’ interaction in the determines the actors' ability to switch to active social networking services using the Rössler actions as a result of destructive information irregular attractor is formalized as a system of influence and is formed as a result of individual differential equations [19] 𝑑𝐼 (𝑡) characteristics; 𝑏 is a parameter that determines = 𝛾𝑅 (𝑡) + 𝜃𝑍(𝑡); the actors' ability to switch to chaotic dynamics 𝑑𝑡 under the influence of destructive information 𝑑𝑅(𝑡) influence. = 𝜉𝐼 (𝑡) + 𝜇𝑅 (𝑡); (1) 𝑑𝑡 To simulate the interaction of actors in the SIS 𝑑𝑍 (𝑡) based on the synthesized model (1) were used the ( ) ( ) ( ) { 𝑑𝑡 = 𝑎 + 𝐼 𝑡 𝑍 𝑡 − 𝑏𝑍 𝑡 , tools of Google Collaboratory environment and where 𝐼(𝑡) is the destructive information programming language Python. The bifurcation influence, which is carried out by the opposing diagram of the system of differential equations (1) group in the social networking services at values of parameters 𝛾 = 1, 𝜉 = 1, 𝜃 = 1, 𝜇 = information space; 𝑅(𝑡) is the function which 0.2, 𝑎 = 0.2, 𝑏 = {1; 10} is constructed, which is characterizes the actors' ability to critically presented in Figure 2. perceive the content and determines the level of Figure 2: Bifurcation diagram of the Rössler attractor Rössler bifurcation diagram is similar in nature 2.2. Determination of the and behavior to the logistic transformation bifurcation diagram (Figure 2 a, b) [20, 21] chaotization metric of the system 𝑥𝑛+1 = 𝑟𝑥𝑛 (1 − 𝑥𝑛 ). (2) based on entropy To simplify the calculations, we further system is a senior Lyapunov exponent. Despite analyze the behaviour of Rössler system in the 𝑍- the developed mathematical apparatus associated plane based on the analysis of the bifurcation with the study of dynamical systems and their diagram of the logistic transformation. behaviour based on Lyapunov exponents, this It is known from analysis of sources [22, 23] approach has an analytical character. In practice, that a marker of chaotic dynamics appearance in a it leads to post-analysis based on a statistical retrospective analysis of the system parameters. (a) the control parameter 𝑟 ∈ (2.5; 4); (b) the control parameter 𝑟 ∈ (3.8; 4); Figure 3: Bifurcation diagram of the logistic transformation It is well known that the bifurcation diagram in sequence of "slices" into the sequence of its physical sense describes possible states of the estimates of kernels of normalized probability system depending on the control parameter 𝑟 [24- density distribution – 𝑝𝑖 (𝑥). 26]. Each "slice" of the bifurcation diagram To determine the entropy of the system at {𝑋𝑖 (𝑟)} describes a set of system states 𝑥𝑖𝑗 ∈ known values of the probability density 𝑋𝑖 (𝑟), 𝑗 ∈ (1; 𝑖𝑛𝑓) is the number of system states distribution, we use the expression for Shannon's in the 𝑗-th "slice" of the bifurcation diagram. We entropy [28] will determine the entropy of the system based on a preliminary analysis of the probability density 𝐸𝑖 = − ∫ 𝑝𝑖 (𝑥 )𝑙𝑜𝑔2 (𝑝𝑖 (𝑥 ))𝑑𝑥. (3) of states 𝑆𝑖𝑗 , for this purpose we use the Thus, for each set of states 𝑋𝑖 (𝑟) the entropy mathematical apparatus KDE (Kernel Density 𝐸𝑖 is obtained. The variation of the entropy value Estimation) [27]. Therefore, we transform the is shown in Figure 4. (a) the control parameter 𝑟 ∈ (2.5; 4); (b) the control parameter 𝑟 ∈ (3.8; 4); Figure 4: Shannon's entropy for the logistic mapping at different values of the parameter 𝑟 3. Modelling results accompanied by a rapid increase in the value of entropy 𝑑𝐸 The analysis of the bifurcation diagram and ≫ 𝑀. 𝑑𝑡 entropy suggests the following: 1. Local maximums of entropy are observed at 4. In the field of chaotic dynamics of actors’ bifurcation points, which is interpreted by a interaction in the social networking services, the temporal increase in uncertainty. It can be related entropy of the system tends to the maximum, as to an abrupt change in the behaviour of social the probability density distribution approaches networking services’ actors because of destructive uniformity. If the number of states of the virtual information influence on virtual communities community of actors is 𝑁, then under the [29, 30]. Actors need some transition period to conditions of transition to chaotic dynamics form their viewpoint on the events in the 𝑁 → ∞. In this case, the probability of being the information space to further interact with other virtual community in one of these states is defined actors and virtual communities. as uniform distribution 2. The life cycle of the virtual community of 1 𝑝= actors in social networking services is followed by 𝑁 changes in indicators of their interaction from Then the entropy is defined as stationary (characterized by a decrease in entropy 𝑁 𝑁 value) to chaotic dynamics (entropy growth). The 1 1 𝐸 = − ∑ 𝑝𝑖 log 2 𝑝𝑖 = − ∑ log 2 . result of passing the bifurcation point by the 𝑁 𝑁 𝑖=1 𝑖=1 system is structural changes in virtual From where communities – the number of participants, 𝑁 creation of new associations, interaction through 1 1 likes, reposts and distribution of given content. 𝐸 (𝑁 → ∞) = lim (− ∑ log 2 ) = 𝑁→∞ 𝑁 𝑁 3. The transition of actor interactions in the 𝑖=1 social networking services to chaotic dynamics is 1 = lim (−𝑁 log 2 𝑁) = lim log 2 𝑁. 𝑁→∞ 𝑁 𝑁→∞ 4. Practical guidelines identify periods of growth. Thus, the analysis of entropy value dynamics changes indicates a transition of virtual community to chaotic Considering the results of the modelling of dynamics and promptly applies methods of its actor interactions in virtual communities, the suppression. following practical recommendations for identifying precursors of chaotic dynamics are given: 6. References 1. Applying Rössler chaotic system for modelling actors' interaction in social networking [1] Liu Y., Ni X., and Niu G. “The influence of services under the destructive information active social networking services use and influence and conduct of information social capital on flourishing in Chinese confrontation allows describing the transition of adolescents.” Children And Youth Services citizens' potential to active actions in real life. 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