nitial conditions are at a fixed point, we know
      that $x(\infty)$ will be at the same fixed point.</p>

      <p>Next let's investigate the behavior of the system in the local vicinity
      of the fixed points.  Examining the fixed point at $x^* = \pi$, if the
      system starts just to the right of the fixed point, then $\dot{x}$ is
      positive, so the system will move away from the fixed point.  If it starts
      to the left, then $\dot{x}$ is negative, and the system will move away in
      th