Disclaimer. The is admittedly a soft question. If it does not meet the criteria for being an acceptable MO question, I apologize in advance.
I'll soon be teaching a (basic) course on mathematical control theory. The first part of the course will focus on mathematical modelling of dynamical systems. More precisely, I will present examples of mathematical models of dynamical systems encountered in engineering, physics, biology, etc., and discuss some of their basic properties (e.g., existence of equilibria, stability, etc.)
Now, examples that are commonly used include: damper-spring-mass system, RLC circuits, pendulum, etc. However, I would like to come up with something different. Thus, I was thinking about models used to describe unconventional/unusual dynamical phenomena.
Examples of "unconventional" modelling that came to my mind are, for instance, dynamical models of love or hate displayed by individuals in a romantic relationship (see, e.g., this paper). However, I'm curious to hear about more unconventional examples. Thanks in advance for your input!