0%" src="figures/pend_sinx_annotated.svg"/>
      </figure>

      <p> For instance, we can see that any initial condition $x(0) \in
      (-\pi,\pi)$ will result in $\lim_{t\rightarrow \infty} x(t) = 0$.  This
      region is called the <em>region of attraction</em> (or <em>basin of
      attraction</em>) of the fixed point at $x^* = 0$. Basins of attraction of
      two fixed points cannot overlap, and the manifold separating two basins
      of attraction is called the <em>separatrix</em>. Here the unsta