On the basin of attraction of limit cycles in periodic differential equations (Q879694)

Summary: We consider a general system of ordinary differential equations \(\dot x=f(t,x)\), where \(x\in\mathbb{R}^n\), and \(f(t+T,x)=f(t,x)\) for all \((t, x)\in\mathbb{R}\times\mathbb{R}^n\) is a periodic function. We give a sufficient and necessary condition for the existence and uniqueness of an exponentially asymptotically stable periodic orbit. Moreover, this condition is sufficient and necessary to prove that a subset belongs to the basin of attraction of the periodic orbit. The condition uses a Riemannian metric, and we present methods to construct such a metric explicitly.