In Nonlinear dynamics, specially refering to strogatz book) what does he mean by $\dot{x}$?

Question

What is the difference between $\dot x$ and f(x), I mean he uses the two interchangeably, especially in example 2.5.1 on page 27. I know that $\dot x$ means the derivative of x with respect to time; $\frac{dx}{dt}$, but is the x a function of t? like does it mean $\frac{dx(t)}{dt}$?

Answer 1

Yes, $x$ is a function of $t$. Therefore, it is the derivative of the function $x(t)$ with respect to time, as you've correctly indicated. This notation is originally from Newton and, while compact, is only appropriate if the variable that you are differentiating w.r.t. is unambiguous.