This is an ongoing account of the process of building a model of the UK Retail Market as a Predator-Prey System. The situation is modelled from several viewpoints and then triangulated. Initially it will be modelled theoretically using the Lotka–Volterra equations modified for finite resources, multiple predators and multiple prey. Then Particle Swarm Optimisation (PSO) methods and ML will be used to produce a more substantive predictive analytics model of the UK Retail Market.
As a first approximation the Lotka-Volterra equations with stochastic noise were used. The results are qualitatively reasonable as shown below:
The next steps will be to add interactive elements to the Jupyter notebook using ipywigets so that so that the parameters can be adjusted to match the empirical data available from the ONS. Additionally multiple companies and corporation in competition will be added to the model as well as a finite customer base so that the model has a higher quantitative accuracy. An initial Jupyter notebook to perform this non-linear ODE numerical analysis is presented below: