# existence of closed orbits versus global stability of a system

Using Dulac's criterion one can prove that a system has no closed orbits. Does it have any applicability for the global stability of a system?

Please help me to understand the relation between a system having no closed orbits versus the global stability of the system. Which one implies the other or are they equivalent? I am a beginner of this topic. Thanks in advance.

• Counterexample: $x'=x$. – John B Sep 19 '17 at 7:34