On the basin of attraction of limit cycles in periodic differential equations

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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