New models for the analysis and forecasting of the dynamics in complex social systems

Abstract

The thesis is focused on developing stochastic models of transitions between states in complex social systems, which are defined as networks of relationships between individuals, groups and organisations. The methods developed in this thesis are non-disciplinary. They can be used in many contexts because random (or ‘stochastic’) processes occur in many various systems – e.g. physical, biological and financial.

The modelling approach is new, working with system-level parameters, avoiding reference to node-level changes and modelling a non-Markov process by including self-organisation and the effects (memory) of previous system states over a configurable number of time intervals. In this thesis, we investigated three cases referred to as Cases A, B and C. The developed model reappears in every case. Case A considers the processes of information transmission in social systems (social networks); Case B studies random shifts in electoral preferences during election campaigns; Case C models random behaviour of financial indexes on the stock exchange stock exchange.

To design a stochastic dynamics model of changing voter preferences, we evaluated probability models for transitions between possible system states for each of the cases, formulated the boundary task for probability density functions and derived a second-order non-linear differential equation incorporating self-organisation and memory. The implications of the new models were tested using specially developed computer software. Each developed model enabled us to create an algorithm which can be easily put into practice for a) monitoring the dynamics of viewpoints in society, b) modelling electoral processes and c) developing investment strategies and aiding decision-making.