A dynamical system (https://en.wikipedia.org/wiki/Dynamical_system) is basically a bunch of (continuous / discrete) variables whose evolution is governed by a set of (differential / difference) equations. E.g. a pendulum is a dynamical system whose state can be described with a single variable 𝜃 (the angle of the pendulum), governed by the differential equation:
𝘥²𝜃/𝘥t² + g/l sin(𝜃) = 0
(where g is the gravitational acceleration and l is the length of the pendulum)
Dynamical systems whose behaviour is linear are kinda well-behaving and easy to analyse. (linear in this context means that the system's response to a linear combination of inputs will be the same as the linear combination of its responses to the individual inputs) Non-linear systems on the other hand behave chaotically, producing wildly different responses to slight differences in their inputs.
