Mathematical and Computer Models of Message Distribution in Social Networks Based on the Space Modification of Fermi-Pasta-Ulam Approach

Abstract

The article proposes a new class of models for message distribution in social networks based on specific systems of differential equations, which describe the information distribution in the chain of the network graph. This class of models allows to take into account specific mechanisms for transmitting messages. Vertices in such graphs are individuals who, receiving a message, initially form their attitude towards it, and then decide on the further transmission of this message, provided that the corresponding potential of the interaction of two individuals exceeds a certain threshold level. Authors developed the original algorithm for calculating time moments of message distribution in the corresponding chain, which comes to the solution of a series of Cauchy problems for systems of ordinary nonlinear differential equations. These systems can be simplified, and part of the equations can be replaced with the Boussinesq or Korteweg-de Vries equations. The presence of soliton solutions of the above equations provides grounds for considering social and communication solitons as an effective tool for modeling processes of distributing messages in social networks and investigating diverse influences on their dissemination.