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

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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
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

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