Could you comment on what has been the two-dimensional differential equation (with field of vectors of class $C^1$) whose phase portrait is strange or unusual?
For example in this article I found the following:
\begin{align}
\dot{r}&=-(r-1)^5\\
\dot{\theta}&=\left\{
\begin{array}{lcc}
0&,&r=1\\
-(r-1)^3\sin\left(\dfrac{3}{2(r-1)}\right)&,&r\ne 1
\end{array}
\right.
\end{align}
whose phase portrait is:
When I think of something strange, many things come to mind, such as:
