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Complexity
Volume 2018, Article ID 4732491, 11 pages
https://doi.org/10.1155/2018/4732491
Research Article

Complexity of a Microblogging Social Network in the Framework of Modern Nonlinear Science

School of Business Informatics, National Research University Higher School of Economics, Moscow 101000, Russia

Correspondence should be addressed to Andrey Dmitriev; ur.esh@veirtimd.a

Received 9 August 2018; Accepted 11 November 2018; Published 2 December 2018

Guest Editor: Piotr Brodka

Copyright © 2018 Andrey Dmitriev et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Recent developments in nonlinear science have caused the formation of a new paradigm called the paradigm of complexity. The self-organized criticality theory constitutes the foundation of this paradigm. To estimate the complexity of a microblogging social network, we used one of the conceptual schemes of the paradigm, namely, the system of key signs of complexity of the external manifestations of the system irrespective of its internal structure. Our research revealed all the key signs of complexity of the time series of a number of microposts. We offer a new model of a microblogging social network as a nonlinear random dynamical system with additive noise in three-dimensional phase space. Implementations of this model in the adiabatic approximation possess all the key signs of complexity, making the model a reasonable evolutionary model for a microblogging social network. The use of adiabatic approximation allows us to model a microblogging social network as a nonlinear random dynamical system with multiplicative noise with the power-law in one-dimensional phase space.