The Verhulst-Like Equations: Integrable OΔE and ODE with Chaotic Behavior

In this paper, we study various variants of Verhulst-like ordinary differential equations (ODE) and ordinary difference equations (O Δ E). Usually Verhulst ODE serves as an example of a deterministic system and discrete logistic equation is a classic example of a simple system with very complicated (chaotic) behavior. In our paper we present examples of deterministic discretization and chaotic continualization. Continualization procedure is based on Padé approximants. To correctly characterize the dynamics of obtained ODE we measured such characteristic parameters of chaotic dynamical systems as the Lyapunov exponents and the Lyapunov dimensions. Discretization and continualization lead to a change in the symmetry of the mathematical model (i.e., group properties of the original ODE and O Δ E). This aspect of the problem is the aim of further research.

PROCESS MODELING OF MESSAGE DISTRIBUTION IN SOCIAL NETWORKS BASED ON SOCIO-COMMUNICATIVE SOLITONS

The article proposes a new class of models for distributing messages in social networks based on socio- communicative solitons. This class of models allows to take into account the specific mechanisms for transmitting messages in the chains of the network graph, in which each of the vertices 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. The authors developed the original algorithm for calculating the 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. A special continualization procedure is formulated, which makes it possible to simplify substantially the resulting system of equations and replace a part of the equations by the Boussinesq or Korteweg-de Vries equations. The presence of soliton solutions to the above-mentioned equations provides grounds for considering socio-communicative solitons as an effective tool for modeling the processes of distributing messages in social networks and investigating the diverse influences on their dissemination processes.