Year of Graduation
Investigation into the Regular and Chaotic States of Twitter as a Dissipative System
Sociophysical modeling of social networks is one of the promising areas of its research. The main drawback of existing models is the fact that they are not able to report the presence of regular and chaotic states of the social network. Therefore, the goal is to create an adequate mathematical model of Twitter as a dissipative system that determines its regular and chaotic states. As a result of the research, a three-dimensional model of Twitter is constructed as a dissipative system with one controlling parameter (the intensity of the external information), which allows to explain the network's striving for a stable equilibrium state with its small value and the ability of the network to generate low-dimensional chaos in case the value of the control parameter increases to a critical value. It is noticed that this model is an adequate heuristic model explaining the fundamental properties of the social network: fractality, randomness, persistence and positive memory of the time series of Twitter. It is shown that Kaulakis' nonlinear random dynamical system describing the formation of Twitter signals is a more adequate model: in addition to the possibility of explaining the above fundamental properties of the network, this model gives a good correspondence between the theoretical and observed fine structure of the time series of Twitter. It is revealed that this system describes the formation of Twitter signals with 1⁄f^β noise, which is a necessary condition for the emergence of self-organized criticality of the network and the potential propensity of the network to catastrophic events. In this case, the use of Tsallis entropy allows to describe Twitter as a social network, in which the interaction of each user of the network with the entire social network is fundamentally important.