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 selforganization 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.
The growing influence of social networking
services on social communication processes has
turned them into a leading channel of
communication [
Analysis of recent research and publications
[
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
solving the problem of modelling actors'
interaction in virtual communities of services, not
only the synthesis of control actions but also the
point in time at which such a measure is
implemented, is of particular importance. This
approach will make it possible to suppress chaotic
dynamics of interaction and form prerequisites for
effective counteraction to threats to state
information security in the social networking
services [
The purpose of the article is to determine a point in time for effective implementation of the control action, followed by the transition of virtual communities of actors in the social networking services from chaotic interaction with a given state, in which the levelling of destructive information influence the actors is ensured.
To achieve the goal, the following tasks are required:
1) Formalize the interaction of actors in virtual communities of social networking services under the influence of threats using irregular attractors.
2) Estimate system entropy using kernel density estimation of actor interaction parameters in social networking services.
3) Identify existing precursors of chaotic dynamics of actors' interaction in the social networking services and give practical recommendations for their early identification.
In the case of transition of social networking services actors' interaction to deterministic chaos, it is characterized by the high sensitivity of virtual communities to changes in system parameters and the action of disturbances, in particular destructive information influences. Even if the interaction of actors in the social networking services is formalized by deterministic models, in a state of deterministic chaos, their communication turns into random and unpredictable processes (Figure 1).
To describe the interaction of actors in the social networking services when the system transitions to chaotic dynamics, it is advisable to use irregular attractors. Even though social networking services is a dissipative system, which can be either open or non-equilibrium, using the irregular attractors is appropriate.
The features of irregular attractors are the
complex geometric structure of the set of states of
the system they describe. Such attractors are
characterized by a simultaneous combination of
both stability and instability. Therefore, irregular
attractors provide a high degree of adequacy in
describing the interaction of actors in the social
networking services, which are taking place under
the conditions of information confrontation. Such
attractors include Lorenz attractors, Rössler
attractors, and others [
In general terms, the actors’ interaction in the
social networking services using the Rössler
irregular attractor is formalized as a system of
differential equations [
To simulate the interaction of actors in the SIS
based on the synthesized model (1) were used the
tools of Google Collaboratory environment and
programming language Python. The bifurcation
diagram of the system of differential equations (1)
at values of parameters = 1, = 1, = 1, =
0.2, = 0.2, = {1; 10} is constructed, which is
presented in Figure 2.
Rössler bifurcation diagram is similar in nature
and behavior to the logistic transformation
bifurcation diagram (Figure 2 a, b) [
To simplify the calculations, we further analyze the behaviour of Rössler system in the plane based on the analysis of the bifurcation diagram of the logistic transformation.
It is known from analysis of sources [
It is well known that the bifurcation diagram in
its physical sense describes possible states of the
system depending on the control parameter
[2426]. Each "slice" of the bifurcation diagram
{ ( )} describes a set of system states ∈
( ), ∈ (1; ) is the number of system states
in the -th "slice" of the bifurcation diagram. We
will determine the entropy of the system based on
a preliminary analysis of the probability density
of states , for this purpose we use the
mathematical apparatus KDE (Kernel Density
Estimation) [
To determine the entropy of the system at known values of the probability density distribution, we use the expression for Shannon's entropy [28] = − ∫ ( ) 2( ( )) .
(3)
Thus, for each set of states ( ) the entropy is obtained. The variation of the entropy value is shown in Figure 4. (b) the control parameter ∈ (3.8; 4);
The analysis of the bifurcation diagram and entropy suggests the following:
1. Local maximums of entropy are observed at bifurcation points, which is interpreted by a temporal increase in uncertainty. It can be related to an abrupt change in the behaviour of social networking services’ actors because of destructive information influence on virtual communities [29, 30]. Actors need some transition period to form their viewpoint on the events in the information space to further interact with other actors and virtual communities.
2. The life cycle of the virtual community of actors in social networking services is followed by changes in indicators of their interaction from stationary (characterized by a decrease in entropy value) to chaotic dynamics (entropy growth). The result of passing the bifurcation point by the system is structural changes in virtual communities – the number of participants, creation of new associations, interaction through likes, reposts and distribution of given content.
3. The transition of actor interactions in the social networking services to chaotic dynamics is accompanied by a rapid increase in the value of entropy
4. In the field of chaotic dynamics of actors’ interaction in the social networking services, the entropy of the system tends to the maximum, as the probability density distribution approaches uniformity. If the number of states of the virtual community of actors is , then under the conditions of transition to chaotic dynamics
→ ∞. In this case, the probability of being the virtual community in one of these states is defined as uniform distribution = 1 →∞ 1 =1 From where Then the entropy is defined as = − ∑ log2 = − ∑ log2 . ( → ∞) = lim ( − ∑ log2 ) = = lim (− →∞ log2 ) = lim log2 .
→∞ =1 =1 1 1 1 1
Considering the results of the modelling of actor interactions in virtual communities, the following practical recommendations for identifying precursors of chaotic dynamics are given:
1. Applying Rössler chaotic system for modelling actors' interaction in social networking services under the destructive information influence and conduct of information confrontation allows describing the transition of citizens' potential to active actions in real life. Therefore, it is reasonable to apply the proposed approach to modelling interactions in virtual communities when developing and improving the subsystem of information space monitoring within the framework of the state information security system in the social networking services.
2. The simulation of virtual communities in the social networking services based on the chaotic Rössler system is appropriate for monitoring the interaction of groups of actors created and/or managed by an opposing force. Actors of such virtual communities are potentially used to participate in mass protests and unrest in real life. Therefore, timely identification of signs of their transition to chaotic dynamics based on entropy indicator (3) will allow responding in advance to changes in the situation in the social networking services information space.
Simulation of actors' interaction in the social networking services based on irregular attractors investigates the processes of transition of communication in the information space of services into chaotic dynamics, in which associations of actors become unmanageable. The application of irregular attractors helps considering the effect of destructive information influence on actors in the social networking services in the conditions of information confrontation. To achieve this, interaction in the information space of services is modelled using the Rössler irregular attractor, which enables the formalization of interaction not only online but also the transition of actors to acts of defiance in real life. For early detection of signs of transition to chaotic dynamics, we propose to use the kernel density estimation of the entropy distribution of interaction parameters of actors in the social networking services to determine its dynamics to identify periods of growth. Thus, the analysis of entropy value dynamics changes indicates a transition of virtual community to chaotic dynamics and promptly applies methods of its suppression.
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