Giesl, Peter (2004) On the basin of attraction of limit cycles in periodic differential equations. Zeitschrift fur Analysis und ihre Anwendungen, 23 (3). pp. 547-576. ISSN 0232-2064
Full text not available from this repository.Abstract
We consider a general system of ordinary differential equations (x) over dot = f (t, x), where x is an element of R-n, and f (t + T, x) = f (t, x) for all (t, x) is an element of R x 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.
Item Type: | Article |
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Schools and Departments: | School of Mathematical and Physical Sciences > Mathematics |
Depositing User: | Peter Giesl |
Date Deposited: | 06 Feb 2012 21:09 |
Last Modified: | 10 Jul 2012 14:31 |
URI: | http://sro.sussex.ac.uk/id/eprint/29847 |