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Necessary condition for the basin of attraction of a periodic orbit in non-smooth periodic systems
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.
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Publication status
- Published
Journal
Discrete and Continuous Dynamical Systems - Series AISSN
1078-0947Publisher
American Institute of Mathematical SciencesExternal DOI
Issue
2-3Volume
18Page range
355-373Pages
19.0Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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