Solution
= Solution
For $a=-1,b=1$, $\dot y=-1+x-y-x^2-y^2\le-1/2<0$ after maximizing the two quadratic expressions. Thus no orbit is periodic. A proper forward bounding region or Lyapunov trapping <function> would, in a planar flow with no equilibria, force a periodic <limit> set by Poincare-Bendixson; therefore no such global bounding <function> exists.