Flows on the Line
Here x ( t ) is a real-valued function of time t, and f ( x ) is a smooth real-valued function of x. We’ll call such equations one-dimensional or first-order systems.
Before there’s any chance of confusion, let’s dispense with two fussy points of terminology:
1. The word system is being used here in the sense of a dynamical system, not in the classical sense of a collection of two or more equations. Thus a single equation can be a “system.”