Chapter 7.1, Problem 3E

Interpretation Introduction

Interpretation:

To sketch the portrait for the system equation ${\dot{\text{r}}\text{ = r (1- r}}^2{\text{)(4 - r}}^2\text{), }\dot{\theta }{\text{ = 2 - r}}^2$, where $\text{r}$ and $\theta$ are polar co-ordinates.

Concept Introduction:

Fixed points are the points where $\dot{\text{r}}\text{ = 0}$.

If $\text{r*}$ is the fixed point of the system, then all stable trajectories are inside the circle $\text{r*}$.