Necessary condition for the basin of attraction of a periodic orbit in non-smooth periodic systems

Giesl, Peter (2007) Necessary condition for the basin of attraction of a periodic orbit in non-smooth periodic systems. Discrete and Continuous Dynamical Systems - Series A, 18 (2-3). pp. 355-373. ISSN 1078-0947

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Abstract

We study a time-periodic non-smooth differential equation (x)over dot = f(t,x), x is an element of R. In [4] we have presented a sufficient condition for existence, uniqueness, stability and the basin of attraction of a periodic orbit in such a system, which is a generalized Borg's condition. In this paper we prove that this condition is necessary. The proof involves a generalization of Floquet exponents for periodic orbits of non-smooth differential equations.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Peter Giesl
Date Deposited: 06 Feb 2012 20:49
Last Modified: 10 Jul 2012 11:47
URI: http://sro.sussex.ac.uk/id/eprint/28360
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