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Bass diffusion model, Bass competition model, visualization software, stability analysis, nullcline method, phase portrait, project-based teaching


Marketing | Mathematics | Ordinary Differential Equations and Applied Dynamics | Science and Mathematics Education


Many examples of 2x2 nonlinear systems in a first-course in ODE or a mathematical modeling class come from physics or biology. We present an example that comes from the business or management sciences, namely, the Bass diffusion model. We believe that students will appreciate this model because it does not require a lot of background material and it is used to analyze sales data and serve as a guide in pricing decisions for a single product. In this project, we create a 2x2 ODE system that is inspired by the Bass diffusion model; we call the resulting system the Bass Competition Model. We apply this model to investigate the competition between two smartphone brands, Apple and Samsung. We use existing data that capture social behavior of the users to further investigate the competition dynamics between Apple and Samsung. The goal is to present an example of a competition model that uses real data on a topic that is relatable to the 21st-century student.



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