Generative eBooks

An invitation through embedded visual interactive digital experiments

# Part I: One-dimensional systems: flows on the line

We focus on one-dimensional systems, that is, differential equations of the form

$$\dot{x}=f(x)$$

where $x\in\mathbb{R}$ and $\, f:\mathbb{R}\to\mathbb{R}$. The behavior of solutions of such equations appears to be rather boring at first sight. However, one-dimensional systems are useful to introduce several key ideas that one can generalize in higher dimension. What really makes one-dimensional systems worth studying is bifurcations, that is, how the behavior of solutions changes qualitatively as we modify some parameter of the system.