The short version: A dynamical system is a mathematical structure with a set of variables and a description of how they interact over time. Some of these systems converge onto what are called “attractor basins”, where many variables are simultaneously in an unusual and persistent state, but no particular variable can be singled out as the cause. This might be a fruitful way of thinking of psychiatric disorders.
Some of the other pages on this site describe conditions as “dynamical systems”, complicated combinations of many variables interacting in nonlinear ways that produce chaotic effects. I think almost everyone is implicitly working off this hypothesis, but the only people I can find who discuss it openly are a Dutch team centered around Borsboom et al, and even they don’t think of it exactly the same way I do. This page is intended as a gentle introduction to these kinds of systems. It will start with a more mathematical explanation, then move on to a long and bizarre metaphor which I hope will give you some of the same intuitions I have even if you don’t entirely get the math. I’m not a mathematician, not an expert in dynamical systems, and I may be getting some or all of this wrong.
Imagine Alice has a chronic disease. Luckily, as long as she has a job, she will have health insurance. And health insurance provides her with a treatment. Every day she takes the treatment, her health will go up one point on a 0-100 scale; every day she misses the treatment, it will go down one point. If her health ever gets below 75, she will be too ill to work.