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

journal contribution
posted on 2023-06-08, 09:01 authored by Peter GieslPeter Giesl
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.

History

Publication status

  • Published

Journal

Zeitschrift fur Analysis und ihre Anwendungen

ISSN

0232-2064

Publisher

European Mathematical Society

Issue

3

Volume

23

Page range

547-576

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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