On the Basin of Attraction of Limit Cycles in Periodic Differential Equations
Peter Giesl
TU München, Germany
![On the Basin of Attraction of Limit Cycles in Periodic Differential Equations cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-zaa-volume-23-issue-3.png&w=3840&q=90)
Abstract
We consider a general system of ordinary differential equations
where , and for all 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.
Cite this article
Peter Giesl, On the Basin of Attraction of Limit Cycles in Periodic Differential Equations. Z. Anal. Anwend. 23 (2004), no. 3, pp. 547–576
DOI 10.4171/ZAA/1210