ABSTRACT
At the most basic level, a dynamical system is simply something that evolves deterministically over time. In this context, deterministic means that the system changes by rules that are fixed and not random. Dynamical systems arise in an incredibly wide variety of applications. In ecology, models of population growth are often discrete dynamical systems. The model is a function that uses the population at one generation to compute the population of the next generation. The motion of a pendulum is a continuous dynamical system with the angular position and angular momentum determined at every time. Discrete dynamical systems are incredibly useful for modeling real-world phenomena that occur in discrete time steps.
