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Unbounded basins of attraction of limit cycles
Consider a dynamical system given by a system of autonomous ordinary differential equations. In this paper we provide a sufficient local condition for an unbounded subset of the phase space to belong to the basin of attraction of a limit cycle. This condition also guarantees the existence and uniqueness of such a limit cycle, if that subset is compact. If the subset is unbounded, the positive orbits of all points of this set either are unbounded or tend to a unique limit cycle.
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Publication status
- Published
Journal
Acta Mathematica Universitatis ComenianaeISSN
0862-9544Publisher
Acta Mathematica Universitatis ComenianaeIssue
1Volume
72Page range
81-110Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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