Modelling the stochastic dynamics of transitions between states in social systems incorporating self-organization and memory

This conceptual research presents a new stochastic model of the dynamics of state-to-state transitions in social systems, the Zhukov–Khvatova model. Employing a mathematical approach based on percolation theory the model caters for random changes, system memory and self-organisation. Curves representing the approach of the system to the percolation threshold differ significantly from the smooth S-shaped curves predicted by existing models, showing oscillations, steps and abrupt steep gradients. 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. Computational modelling is used to demonstrate how the percolation threshold (i.e. the share of nodes which allows information to spread freely within the network) is reached. Possible applications of the model discussed include modelling the dynamics of viewpoints in society during social unrest and elections, changing attitudes in social networks and forecasting the outcome of promotions or uptake of campaigns. The easy availability of system level data (network connectivity, evolving system penetration) makes the model a particularly valuable addition to the toolkit for social sciences, politics, and potentially marketing.